%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO563+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:25:15 PM UTC 2026
% Result : Theorem 5.54s 1.18s
% Output : CNFRefutation 5.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 23
% Syntax : Number of formulae : 132 ( 29 unt; 0 def)
% Number of atoms : 329 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 327 ( 130 ~; 125 |; 48 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-3 aty)
% Number of variables : 616 ( 588 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [A,B,C,O,M] :
( ( eqangle(A,B,A,C,O,B,O,M)
& coll(M,B,C)
& circle(O,A,B,C) )
=> midp(M,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [A,B,C,D] :
? [O] :
( ( cyclic(A,B,C,D)
& perp(A,C,C,B) )
=> circle(O,A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [Q,R,P,O1,S,Y,O,X,I,NWPNT1,NWPNT2] :
( ( coll(I,Y,X)
& coll(I,R,S)
& circle(O,Q,X,NWPNT2)
& circle(O,Y,P,Q)
& coll(Y,Q,S)
& circle(O1,Q,S,NWPNT1)
& circle(O1,Q,R,P) )
=> eqangle(R,I,I,X,R,P,P,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [Q,R,P,O1,S,Y,O,X,I,NWPNT1,NWPNT2] :
( ( coll(I,Y,X)
& coll(I,R,S)
& circle(O,Q,X,NWPNT2)
& circle(O,Y,P,Q)
& coll(Y,Q,S)
& circle(O1,Q,S,NWPNT1)
& circle(O1,Q,R,P) )
=> eqangle(R,I,I,X,R,P,P,X) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f97,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f98,plain,
! [X0,X1,X2] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f100,plain,
! [X0,X1,X2] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f102,plain,
! [A,C,D] :
( coll(C,D,A)
| ! [B] :
( ~ coll(A,B,D)
| ~ coll(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f113,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f116,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f134,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f135,plain,
! [B,C,D,E] :
( cyclic(B,C,D,E)
| ! [A] :
( ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f138,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f144,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f146,plain,
! [A,B,C,D,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ! [P,Q,U,V] :
( ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ) ),
inference(miniscoping,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f184,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f185,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q] : ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(miniscoping,[status(thm)],[f184]) ).
fof(f186,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f188,plain,
! [A,B,C,D] :
( ! [P,Q] : eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(miniscoping,[status(thm)],[f187]) ).
fof(f189,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f190,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f191,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f194,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f195,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| ~ coll(X0,X3,X2)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f196,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f197,plain,
! [A,B,P,Q] :
( cong(A,B,P,Q)
| ! [C,R] :
( ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ) ),
inference(miniscoping,[status(thm)],[f196]) ).
fof(f198,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f217,plain,
! [A,B,C,O,M] :
( midp(M,B,C)
| ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f218,plain,
! [B,C,M] :
( midp(M,B,C)
| ! [A,O] :
( ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1,X2,X3,X4] :
( midp(X4,X2,X3)
| ~ eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ coll(X4,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [A,B,C,M] :
( cong(A,M,B,M)
| ~ midp(M,A,C)
| ~ perp(A,B,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f221,plain,
! [A,B,M] :
( cong(A,M,B,M)
| ! [C] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C) ) ),
inference(miniscoping,[status(thm)],[f220]) ).
fof(f222,plain,
! [X0,X1,X2,X3] :
( cong(X0,X3,X1,X3)
| ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f231,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f232,plain,
! [X0,X1,X2,X3] :
( perp(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f233,plain,
! [A,B,P,Q] :
( perp(P,A,A,Q)
| ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f234,plain,
! [A,P,Q] :
( perp(P,A,A,Q)
| ! [B] :
( ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ) ),
inference(miniscoping,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cyclic(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f255,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f256,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f331,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f332,plain,
! [A,O] :
( ? [P] : perp(P,A,A,O)
| ! [B,C] : ~ circle(O,A,B,C) ),
inference(miniscoping,[status(thm)],[f331]) ).
fof(f333,plain,
! [A,O] :
( perp(sK11_skl(O,A),A,A,O)
| ! [B,C] : ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(P,sK11_skl(O,A))],[f332]) ).
fof(f334,plain,
! [X0,X1,X2,X3] :
( perp(sK11_skl(X0,X1),X1,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f346,plain,
! [A,B,C,D] :
? [O] :
( circle(O,A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f347,plain,
! [A,B,C] :
( ? [O] : circle(O,A,B,C)
| ! [D] : ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(miniscoping,[status(thm)],[f346]) ).
fof(f348,plain,
! [A,B,C] :
( circle(sK15_skl(C,B,A),A,B,C)
| ! [D] : ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(O,sK15_skl(C,B,A))],[f347]) ).
fof(f349,plain,
! [X0,X1,X2,X3] :
( circle(sK15_skl(X1,X2,X0),X0,X2,X1)
| ~ cyclic(X0,X2,X1,X3)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f348]) ).
fof(f369,plain,
? [Q,R,P,O1,S,Y,O,X,I,NWPNT1,NWPNT2] :
( ~ eqangle(R,I,I,X,R,P,P,X)
& coll(I,Y,X)
& coll(I,R,S)
& circle(O,Q,X,NWPNT2)
& circle(O,Y,P,Q)
& coll(Y,Q,S)
& circle(O1,Q,S,NWPNT1)
& circle(O1,Q,R,P) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [R,P,X,I] :
( ~ eqangle(R,I,I,X,R,P,P,X)
& ? [Y] :
( coll(I,Y,X)
& ? [S] :
( coll(I,R,S)
& ? [Q,O] :
( ? [NWPNT2] : circle(O,Q,X,NWPNT2)
& circle(O,Y,P,Q)
& coll(Y,Q,S)
& ? [O1] :
( ? [NWPNT1] : circle(O1,Q,S,NWPNT1)
& circle(O1,Q,R,P) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK20_skl,sK23_skl,sK23_skl,sK22_skl,sK20_skl,sK21_skl,sK21_skl,sK22_skl)
& coll(sK23_skl,sK24_skl,sK22_skl)
& coll(sK23_skl,sK20_skl,sK25_skl)
& circle(sK27_skl,sK26_skl,sK22_skl,sK30_skl)
& circle(sK27_skl,sK24_skl,sK21_skl,sK26_skl)
& coll(sK24_skl,sK26_skl,sK25_skl)
& circle(sK28_skl,sK26_skl,sK25_skl,sK29_skl)
& circle(sK28_skl,sK26_skl,sK20_skl,sK21_skl) ),
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(R,sK20_skl),skolemize(P,sK21_skl),skolemize(X,sK22_skl),skolemize(I,sK23_skl),skolemize(Y,sK24_skl),skolemize(S,sK25_skl),skolemize(Q,sK26_skl),skolemize(O,sK27_skl),skolemize(O1,sK28_skl),skolemize(NWPNT1,sK29_skl),skolemize(NWPNT2,sK30_skl)],[f370]) ).
fof(f376,plain,
circle(sK27_skl,sK26_skl,sK22_skl,sK30_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f379,plain,
~ eqangle(sK20_skl,sK23_skl,sK23_skl,sK22_skl,sK20_skl,sK21_skl,sK21_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f722,plain,
perp(sK11_skl(sK27_skl,sK26_skl),sK26_skl,sK26_skl,sK27_skl),
inference(resolution,[status(thm)],[f334,f376]) ).
fof(f750,plain,
! [X0,X1] :
( para(X0,X1,sK26_skl,sK27_skl)
| ~ perp(X0,X1,sK11_skl(sK27_skl,sK26_skl),sK26_skl) ),
inference(resolution,[status(thm)],[f722,f117]) ).
fof(f751,plain,
perp(sK26_skl,sK27_skl,sK11_skl(sK27_skl,sK26_skl),sK26_skl),
inference(resolution,[status(thm)],[f722,f114]) ).
fof(f868,plain,
para(sK26_skl,sK27_skl,sK26_skl,sK27_skl),
inference(resolution,[status(thm)],[f751,f750]) ).
fof(f1004,plain,
! [X0,X1] : eqangle(sK26_skl,sK27_skl,X0,X1,sK26_skl,sK27_skl,X0,X1),
inference(resolution,[status(thm)],[f868,f189]) ).
fof(f1361,plain,
! [X0,X1] : eqangle(sK26_skl,sK27_skl,sK26_skl,sK27_skl,X0,X1,X0,X1),
inference(resolution,[status(thm)],[f1004,f144]) ).
fof(f1363,plain,
! [X0,X1] : eqangle(X0,X1,sK26_skl,sK27_skl,X0,X1,sK26_skl,sK27_skl),
inference(resolution,[status(thm)],[f1004,f140]) ).
fof(f2559,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f1363,f186]) ).
fof(f2597,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f2559,f256]) ).
fof(f2674,plain,
! [X0,X1] : coll(X0,X1,X0),
inference(resolution,[status(thm)],[f2597,f100]) ).
fof(f2750,plain,
! [X0,X1] : coll(X0,X0,X1),
inference(resolution,[status(thm)],[f2674,f98]) ).
fof(f2803,plain,
! [X0,X1,X2] :
( coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2750,f103]) ).
fof(f2806,plain,
! [X0,X1,X2] : coll(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f2803,f2750]) ).
fof(f2844,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f2806]) ).
fof(f2846,plain,
! [X0,X1,X2,X3,X4] :
( midp(X4,X2,X3)
| ~ eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f219,f2806]) ).
fof(f2880,plain,
! [X0] : cyclic(sK27_skl,sK27_skl,sK26_skl,X0),
inference(resolution,[status(thm)],[f2844,f1361]) ).
fof(f3313,plain,
! [X0,X1] :
( cyclic(sK27_skl,sK26_skl,X0,X1)
| ~ cyclic(sK27_skl,sK27_skl,sK26_skl,X0) ),
inference(resolution,[status(thm)],[f2880,f136]) ).
fof(f3317,plain,
! [X0,X1] : cyclic(sK27_skl,sK26_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f3313,f2880]) ).
fof(f3323,plain,
! [X0,X1,X2] :
( cyclic(sK26_skl,X0,X1,X2)
| ~ cyclic(sK27_skl,sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f3317,f136]) ).
fof(f3327,plain,
! [X0,X1,X2] : cyclic(sK26_skl,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3323,f3317]) ).
fof(f3385,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ cyclic(sK26_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3327,f136]) ).
fof(f3389,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f3385,f3327]) ).
fof(f3390,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f198,f3389]) ).
fof(f3391,plain,
! [X0,X1,X2] :
( circle(sK15_skl(X1,X2,X0),X0,X2,X1)
| ~ perp(X0,X1,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f349,f3389]) ).
fof(f3393,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f3389]) ).
fof(f3395,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3389]) ).
fof(f3396,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X5,X3)
| ~ eqangle(X2,X0,X2,X1,X4,X5,X4,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3390,f3389]) ).
fof(f3397,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3396,f3389]) ).
fof(f3463,plain,
! [X0,X1] : cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f3395,f3397]) ).
fof(f3464,plain,
! [X0,X1,X2,X3] :
( midp(X3,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f3395,f2846]) ).
fof(f3474,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X1,X2,X3,X0,X3,X2),
inference(resolution,[status(thm)],[f3395,f138]) ).
fof(f3490,plain,
! [X0,X1,X2] :
( perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3463,f3393]) ).
fof(f3502,plain,
! [X0,X1,X2] : perp(X0,X1,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f3490,f3463]) ).
fof(f3551,plain,
! [X0,X1,X2] : circle(sK15_skl(X0,X1,X2),X2,X1,X0),
inference(backward_subsumption_resolution,[status(thm)],[f3391,f3502]) ).
fof(f3555,plain,
! [X0,X1,X2,X3] :
( cong(X1,X0,X3,X0)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f3502]) ).
fof(f3597,plain,
! [X0,X1] : midp(X0,X1,X0),
inference(resolution,[status(thm)],[f3551,f3464]) ).
fof(f3755,plain,
! [X0,X1,X2] : cong(X0,X1,X2,X1),
inference(resolution,[status(thm)],[f3555,f3597]) ).
fof(f4057,plain,
! [X0,X1,X2,X3] :
( perp(X0,X2,X3,X1)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f232,f3755]) ).
fof(f4078,plain,
! [X0,X1,X2,X3] : perp(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f4057,f3755]) ).
fof(f4079,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X4,X5,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f4078]) ).
fof(f4107,plain,
! [X0,X1,X2,X3] : para(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f4079,f4078]) ).
fof(f4113,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3),
inference(backward_subsumption_resolution,[status(thm)],[f189,f4107]) ).
fof(f4150,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( eqangle(X0,X1,X2,X3,X8,X9,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(resolution,[status(thm)],[f4113,f147]) ).
fof(f4315,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X1,X2,X3,X4,X5,X2),
inference(resolution,[status(thm)],[f4150,f3474]) ).
fof(f5057,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f379,f4315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO563+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 17:33:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 5.54/1.18 % Refutation found
% 5.54/1.18 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.54/1.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.54/1.23 % Elapsed time: 0.859999 seconds
% 5.54/1.23 % CPU time: 6.464137 seconds
% 5.54/1.23 % Total memory used: 146.281 MB
% 5.54/1.23 % Net memory used: 140.075 MB
%------------------------------------------------------------------------------