%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO639+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 : n011.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 12:25:26 PM UTC 2026
% Result : Theorem 2.87s 0.81s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 31
% Syntax : Number of formulae : 163 ( 6 unt; 4 def)
% Number of atoms : 486 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 532 ( 209 ~; 207 |; 84 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 5 prp; 0-8 aty)
% Number of functors : 17 ( 17 usr; 16 con; 0-3 aty)
% Number of variables : 705 ( 670 !; 35 ?)
% 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(f5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
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(f10,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(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(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(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
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(f47,axiom,
! [A,B,O] :
( cong(O,A,O,B)
=> eqangle(O,A,A,B,A,B,O,B) ),
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(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(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
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,
! [P,Q,A,N,D,O,B,C,E,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7] :
( ( coll(E,A,N)
& coll(E,P,Q)
& circle(O,D,C,NWPNT7)
& coll(C,Q,A)
& circle(O,D,B,NWPNT6)
& coll(B,P,A)
& circle(O,D,NWPNT4,NWPNT5)
& midp(O,D,A)
& circle(N,P,D,NWPNT3)
& coll(D,A,N)
& circle(N,P,NWPNT1,NWPNT2)
& perp(Q,A,Q,N)
& perp(P,A,P,N)
& ( cong(A,P,A,Q)
| cong(A,P,P,Q) ) )
=> eqangle(A,B,B,E,E,B,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [P,Q,A,N,D,O,B,C,E,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7] :
( ( coll(E,A,N)
& coll(E,P,Q)
& circle(O,D,C,NWPNT7)
& coll(C,Q,A)
& circle(O,D,B,NWPNT6)
& coll(B,P,A)
& circle(O,D,NWPNT4,NWPNT5)
& midp(O,D,A)
& circle(N,P,D,NWPNT3)
& coll(D,A,N)
& circle(N,P,NWPNT1,NWPNT2)
& perp(Q,A,Q,N)
& perp(P,A,P,N)
& ( cong(A,P,A,Q)
| cong(A,P,P,Q) ) )
=> eqangle(A,B,B,E,E,B,B,C) ),
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(f106,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f109,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ para(C,D,E,F)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
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(f118,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f119,plain,
! [A,B,E,F] :
( perp(A,B,E,F)
| ! [C,D] :
( ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
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(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(f148,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
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(f205,plain,
! [A,B,O] :
( eqangle(O,A,A,B,A,B,O,B)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f206,plain,
! [X0,X1,X2] :
( eqangle(X0,X1,X1,X2,X1,X2,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
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(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(f259,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f260,plain,
! [X0,X1,X2] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f259]) ).
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,
? [P,Q,A,N,D,O,B,C,E,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7] :
( ~ eqangle(A,B,B,E,E,B,B,C)
& coll(E,A,N)
& coll(E,P,Q)
& circle(O,D,C,NWPNT7)
& coll(C,Q,A)
& circle(O,D,B,NWPNT6)
& coll(B,P,A)
& circle(O,D,NWPNT4,NWPNT5)
& midp(O,D,A)
& circle(N,P,D,NWPNT3)
& coll(D,A,N)
& circle(N,P,NWPNT1,NWPNT2)
& perp(Q,A,Q,N)
& perp(P,A,P,N)
& ( cong(A,P,A,Q)
| cong(A,P,P,Q) ) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,B,C,E] :
( ~ eqangle(A,B,B,E,E,B,B,C)
& ? [N] :
( coll(E,A,N)
& ? [P,Q] :
( coll(E,P,Q)
& ? [D,O] :
( ? [NWPNT7] : circle(O,D,C,NWPNT7)
& coll(C,Q,A)
& ? [NWPNT6] : circle(O,D,B,NWPNT6)
& coll(B,P,A)
& ? [NWPNT4,NWPNT5] : circle(O,D,NWPNT4,NWPNT5)
& midp(O,D,A)
& ? [NWPNT3] : circle(N,P,D,NWPNT3)
& coll(D,A,N)
& ? [NWPNT1,NWPNT2] : circle(N,P,NWPNT1,NWPNT2)
& perp(Q,A,Q,N)
& perp(P,A,P,N)
& ( cong(A,P,A,Q)
| cong(A,P,P,Q) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK20_skl,sK21_skl,sK21_skl,sK23_skl,sK23_skl,sK21_skl,sK21_skl,sK22_skl)
& coll(sK23_skl,sK20_skl,sK24_skl)
& coll(sK23_skl,sK25_skl,sK26_skl)
& circle(sK28_skl,sK27_skl,sK22_skl,sK35_skl)
& coll(sK22_skl,sK26_skl,sK20_skl)
& circle(sK28_skl,sK27_skl,sK21_skl,sK34_skl)
& coll(sK21_skl,sK25_skl,sK20_skl)
& circle(sK28_skl,sK27_skl,sK32_skl,sK33_skl)
& midp(sK28_skl,sK27_skl,sK20_skl)
& circle(sK24_skl,sK25_skl,sK27_skl,sK31_skl)
& coll(sK27_skl,sK20_skl,sK24_skl)
& circle(sK24_skl,sK25_skl,sK29_skl,sK30_skl)
& perp(sK26_skl,sK20_skl,sK26_skl,sK24_skl)
& perp(sK25_skl,sK20_skl,sK25_skl,sK24_skl)
& ( cong(sK20_skl,sK25_skl,sK20_skl,sK26_skl)
| cong(sK20_skl,sK25_skl,sK25_skl,sK26_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,sK31_skl,sK32_skl,sK33_skl,sK34_skl,sK35_skl]),skolemize(A,sK20_skl),skolemize(B,sK21_skl),skolemize(C,sK22_skl),skolemize(E,sK23_skl),skolemize(N,sK24_skl),skolemize(P,sK25_skl),skolemize(Q,sK26_skl),skolemize(D,sK27_skl),skolemize(O,sK28_skl),skolemize(NWPNT1,sK29_skl),skolemize(NWPNT2,sK30_skl),skolemize(NWPNT3,sK31_skl),skolemize(NWPNT4,sK32_skl),skolemize(NWPNT5,sK33_skl),skolemize(NWPNT6,sK34_skl),skolemize(NWPNT7,sK35_skl)],[f370]) ).
fof(f373,plain,
perp(sK25_skl,sK20_skl,sK25_skl,sK24_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f386,plain,
~ eqangle(sK20_skl,sK21_skl,sK21_skl,sK23_skl,sK23_skl,sK21_skl,sK21_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f448,plain,
perp(sK25_skl,sK24_skl,sK25_skl,sK20_skl),
inference(resolution,[status(thm)],[f114,f373]) ).
fof(f468,plain,
! [X0,X1] :
( para(X0,X1,sK25_skl,sK24_skl)
| ~ perp(X0,X1,sK25_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f117,f373]) ).
fof(f470,plain,
! [X0,X1] :
( perp(X0,X1,sK25_skl,sK24_skl)
| ~ para(X0,X1,sK25_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f120,f373]) ).
fof(f641,plain,
! [X0,X1,X2] :
( cong(X0,X1,X2,X0)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f260,f149]) ).
fof(f656,plain,
! [X0,X1,X2] :
( cong(X2,X0,X0,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f641,f151]) ).
fof(f863,definition,
( sQ20_spl
<=> midp(sK25_skl,sK20_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f865,plain,
( sQ20_spl
| ~ midp(sK25_skl,sK20_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f863]) ).
fof(f978,plain,
! [X0,X1] :
( ~ cong(X0,X0,X0,X1)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f186,f206]) ).
fof(f983,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( eqangle(X4,X5,X6,X7,X2,X3,X8,X9)
| ~ eqangle(X4,X5,X6,X7,X0,X1,X8,X9)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f189,f147]) ).
fof(f984,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f189,f144]) ).
fof(f986,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f189,f140]) ).
fof(f1020,plain,
! [X0,X1,X2,X3] :
( midp(X1,X0,X1)
| ~ coll(X1,X0,X1)
| ~ circle(X3,X2,X0,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f191,f219]) ).
fof(f1039,plain,
para(sK25_skl,sK24_skl,sK25_skl,sK24_skl),
inference(resolution,[status(thm)],[f468,f448]) ).
fof(f1322,plain,
! [X0,X1] :
( ~ midp(X0,X1,X0)
| para(X0,X0,X0,X1) ),
inference(resolution,[status(thm)],[f978,f656]) ).
fof(f1339,definition,
( sQ52_spl
<=> perp(sK25_skl,sK25_skl,sK25_skl,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1340,plain,
( ~ sQ52_spl
| perp(sK25_skl,sK25_skl,sK25_skl,sK24_skl) ),
inference(component_clause,[status(thm)],[f1339]) ).
fof(f1479,plain,
( perp(sK25_skl,sK25_skl,sK25_skl,sK24_skl)
| ~ midp(sK25_skl,sK20_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f1322,f470]) ).
fof(f1487,plain,
( sQ52_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1479,f863,f1339]) ).
fof(f1982,plain,
! [X0,X1] :
( ~ sQ52_spl
| para(X0,X1,sK25_skl,sK24_skl)
| ~ perp(X0,X1,sK25_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f1340,f117]) ).
fof(f3172,definition,
! [X4,X5] :
( sQ172_spl
<=> ~ para(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f3173,plain,
! [X0,X1] :
( ~ sQ172_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3172]) ).
fof(f3185,plain,
( ~ sQ172_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1039,f3173]) ).
fof(f3193,plain,
~ sQ172_spl,
inference(contradiction_clause,[status(thm)],[f3185]) ).
fof(f3307,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f986,f186]) ).
fof(f3318,definition,
! [X2,X3] :
( sQ179_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f3319,plain,
! [X0,X1] :
( ~ sQ179_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f3318]) ).
fof(f3321,plain,
( sQ179_spl
| sQ172_spl ),
inference(split_clause,[status(thm)],[f3307,f3172,f3318]) ).
fof(f3354,plain,
! [X0,X1] :
( ~ sQ179_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3319,f256]) ).
fof(f3373,plain,
! [X0,X1] :
( ~ sQ179_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3354,f100]) ).
fof(f3396,plain,
! [X0,X1] :
( ~ sQ179_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3373,f98]) ).
fof(f3402,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f3396,f103]) ).
fof(f3405,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3402,f3396]) ).
fof(f3410,plain,
! [X0,X1,X2,X3] :
( ~ sQ179_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f3405]) ).
fof(f3491,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3410,f984]) ).
fof(f3508,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3491,f3319]) ).
fof(f3518,plain,
! [X0,X1,X2,X3] :
( ~ sQ179_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f3508,f136]) ).
fof(f3522,plain,
! [X0,X1,X2,X3] :
( ~ sQ179_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3518,f3508]) ).
fof(f3560,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| circle(sK15_skl(X1,X2,X0),X0,X2,X1)
| ~ perp(X0,X1,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f349,f3522]) ).
fof(f3562,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ179_spl
| 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,f3522]) ).
fof(f3563,plain,
! [X0,X1,X2,X3] :
( ~ sQ179_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f3522]) ).
fof(f3564,plain,
! [X0,X1,X2,X3] :
( ~ sQ179_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f3522]) ).
fof(f3565,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ179_spl
| 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)],[f3562,f3522]) ).
fof(f3746,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ179_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f3565,f3522]) ).
fof(f3764,plain,
! [X0,X1] :
( ~ sQ179_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3563,f3746]) ).
fof(f3798,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3764,f3564]) ).
fof(f3801,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3764,f232]) ).
fof(f3806,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3798,f3764]) ).
fof(f3807,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3801,f3764]) ).
fof(f3818,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| circle(sK15_skl(X0,X1,X2),X2,X1,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f3560,f3806]) ).
fof(f3844,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| perp(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f3807,f114]) ).
fof(f3972,plain,
! [X0,X1,X2,X3] :
( ~ sQ179_spl
| midp(X3,X2,X3)
| ~ coll(X3,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1020,f3522]) ).
fof(f3973,plain,
! [X0,X1] :
( ~ sQ179_spl
| midp(X0,X1,X0)
| ~ coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f3972,f3818]) ).
fof(f3980,plain,
! [X0,X1] :
( ~ sQ179_spl
| midp(X0,X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3973,f3405]) ).
fof(f4035,plain,
( sQ20_spl
| ~ sQ179_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f865,f3980]) ).
fof(f4039,plain,
( sQ20_spl
| ~ sQ179_spl ),
inference(contradiction_clause,[status(thm)],[f4035]) ).
fof(f4040,plain,
! [X0,X1] :
( ~ sQ52_spl
| ~ sQ179_spl
| para(X0,X1,sK25_skl,sK24_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1982,f3844]) ).
fof(f4180,plain,
! [X0,X1] :
( ~ sQ52_spl
| ~ sQ179_spl
| para(sK25_skl,sK24_skl,X0,X1) ),
inference(resolution,[status(thm)],[f4040,f107]) ).
fof(f4220,plain,
! [X0,X1,X2,X3] :
( ~ sQ52_spl
| ~ sQ179_spl
| para(X0,X1,X2,X3)
| ~ para(X0,X1,sK25_skl,sK24_skl) ),
inference(resolution,[status(thm)],[f4180,f110]) ).
fof(f4223,plain,
! [X0,X1,X2,X3] :
( ~ sQ52_spl
| ~ sQ179_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4220,f4040]) ).
fof(f4231,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ52_spl
| ~ sQ179_spl
| eqangle(X0,X1,X2,X3,X4,X5,X4,X5) ),
inference(backward_subsumption_resolution,[status(thm)],[f984,f4223]) ).
fof(f4232,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ sQ52_spl
| ~ sQ179_spl
| eqangle(X0,X1,X2,X3,X8,X9,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(backward_subsumption_resolution,[status(thm)],[f983,f4223]) ).
fof(f4667,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ52_spl
| ~ sQ179_spl
| eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(resolution,[status(thm)],[f4232,f4231]) ).
fof(f5039,plain,
( ~ sQ52_spl
| ~ sQ179_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f386,f4667]) ).
fof(f5040,plain,
( ~ sQ52_spl
| ~ sQ179_spl ),
inference(contradiction_clause,[status(thm)],[f5039]) ).
fof(f5041,plain,
$false,
inference(sat_refutation,[status(thm)],[f1487,f3193,f3321,f4039,f5040]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO639+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 18:19:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 2.87/0.81 % Refutation found
% 2.87/0.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.87/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.87/0.85 % Elapsed time: 0.477011 seconds
% 2.87/0.85 % CPU time: 3.442745 seconds
% 2.87/0.85 % Total memory used: 121.201 MB
% 2.87/0.85 % Net memory used: 117.441 MB
%------------------------------------------------------------------------------