%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO597+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:25:20 PM UTC 2026
% Result : Theorem 1.62s 0.67s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 30
% Syntax : Number of formulae : 162 ( 5 unt; 4 def)
% Number of atoms : 434 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 492 ( 220 ~; 207 |; 34 &)
% ( 4 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 5 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 715 ( 701 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [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) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,O,M,N,NWPNT1] :
( ( circle(O,A,N,NWPNT1)
& coll(N,O,M)
& midp(M,B,A)
& circle(O,A,B,C) )
=> eqangle(A,C,C,N,N,C,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,O,M,N,NWPNT1] :
( ( circle(O,A,N,NWPNT1)
& coll(N,O,M)
& midp(M,B,A)
& circle(O,A,B,C) )
=> eqangle(A,C,C,N,N,C,C,B) ),
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(f111,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
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(f121,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f122,plain,
! [X0,X1,X2] :
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f126,plain,
! [A,B,C,D] :
( cyclic(A,B,C,D)
| ! [O] :
( ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ) ),
inference(miniscoping,[status(thm)],[f125]) ).
fof(f127,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cong(X0,X1,X0,X4)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
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(f141,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f142,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
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(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(f250,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f251,plain,
! [C,D,M] :
( midp(M,C,D)
| ! [A,B] :
( ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f250]) ).
fof(f252,plain,
! [X0,X1,X2,X3,X4] :
( midp(X0,X3,X4)
| ~ para(X1,X4,X2,X3)
| ~ para(X1,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f251]) ).
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(f257,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f258,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
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(f272,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f273,plain,
! [A,B,C,D] :
( perp(A,B,C,D)
| ! [P,Q,U,V] :
( ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ) ),
inference(miniscoping,[status(thm)],[f272]) ).
fof(f274,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f273]) ).
fof(f369,plain,
? [A,B,C,O,M,N,NWPNT1] :
( ~ eqangle(A,C,C,N,N,C,C,B)
& circle(O,A,N,NWPNT1)
& coll(N,O,M)
& midp(M,B,A)
& circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,B,C,N] :
( ~ eqangle(A,C,C,N,N,C,C,B)
& ? [O] :
( ? [NWPNT1] : circle(O,A,N,NWPNT1)
& ? [M] :
( coll(N,O,M)
& midp(M,B,A)
& circle(O,A,B,C) ) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK23_skl,sK22_skl,sK22_skl,sK21_skl)
& circle(sK24_skl,sK20_skl,sK23_skl,sK26_skl)
& coll(sK23_skl,sK24_skl,sK25_skl)
& midp(sK25_skl,sK21_skl,sK20_skl)
& circle(sK24_skl,sK20_skl,sK21_skl,sK22_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(A,sK20_skl),skolemize(B,sK21_skl),skolemize(C,sK22_skl),skolemize(N,sK23_skl),skolemize(O,sK24_skl),skolemize(M,sK25_skl),skolemize(NWPNT1,sK26_skl)],[f370]) ).
fof(f373,plain,
midp(sK25_skl,sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f376,plain,
~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK23_skl,sK22_skl,sK22_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f389,plain,
midp(sK25_skl,sK20_skl,sK21_skl),
inference(resolution,[status(thm)],[f122,f373]) ).
fof(f539,plain,
! [X0,X1,X2,X3] :
( ~ midp(X0,X1,X3)
| cyclic(X1,X2,X3,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f127,f260]) ).
fof(f1452,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(f1454,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(f1456,plain,
! [X0,X1,X2] :
( para(X2,X0,X2,X0)
| ~ cyclic(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f191,f186]) ).
fof(f1697,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1452,f274]) ).
fof(f1709,definition,
! [X0,X1,X2,X3] :
( sQ4_spl
<=> ( perp(X0,X1,X2,X3)
| ~ para(X0,X1,X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1710,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| perp(X0,X1,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(component_clause,[status(thm)],[f1709]) ).
fof(f1712,definition,
! [X4,X5] :
( sQ5_spl
<=> ~ perp(X4,X5,X4,X5) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1713,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ perp(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1712]) ).
fof(f1715,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1697,f1709,f1712]) ).
fof(f1809,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1454,f186]) ).
fof(f1818,definition,
! [X0,X1] :
( sQ6_spl
<=> ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1819,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1818]) ).
fof(f1821,definition,
! [X2,X3] :
( sQ7_spl
<=> para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1822,plain,
! [X0,X1] :
( ~ sQ7_spl
| para(X0,X1,X0,X1) ),
inference(component_clause,[status(thm)],[f1821]) ).
fof(f1824,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1809,f1818,f1821]) ).
fof(f1825,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ cyclic(X0,X1,X2,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f1456,f1819]) ).
fof(f1836,plain,
! [X0,X1,X2,X3] :
( ~ sQ6_spl
| ~ midp(X0,X1,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f539,f1825]) ).
fof(f1837,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f260,f1836]) ).
fof(f1874,plain,
( ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f389,f1837]) ).
fof(f1876,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f1874]) ).
fof(f1877,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ7_spl
| perp(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1822,f1710]) ).
fof(f1882,plain,
! [X0,X1] :
( ~ sQ7_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f1822,f256]) ).
fof(f1984,plain,
! [X0,X1] :
( ~ sQ7_spl
| coll(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1882,f100]) ).
fof(f2088,plain,
! [X0,X1] :
( ~ sQ7_spl
| coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f1984,f98]) ).
fof(f2109,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| coll(X1,X2,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2088,f103]) ).
fof(f2112,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| coll(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2109,f2088]) ).
fof(f2113,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f2112]) ).
fof(f2121,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ7_spl
| perp(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f1877,f112]) ).
fof(f2144,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ sQ7_spl
| cong(X1,X0,X2,X0)
| ~ midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f222,f2121]) ).
fof(f2370,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| midp(X0,X2,X2)
| ~ para(X1,X2,X1,X2)
| ~ midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f252,f1822]) ).
fof(f2371,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| midp(X0,X2,X2)
| ~ midp(X0,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2370,f1822]) ).
fof(f2492,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f2112]) ).
fof(f2720,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ para(X1,X0,X1,X0)
| cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2113,f1452]) ).
fof(f2731,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2720,f1822]) ).
fof(f2742,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f2731,f136]) ).
fof(f2746,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2742,f2731]) ).
fof(f2753,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ7_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,f2746]) ).
fof(f2754,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f2746]) ).
fof(f2756,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ7_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)],[f2753,f2746]) ).
fof(f2763,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| eqangle(X0,X1,X2,X1,X0,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2754,f144]) ).
fof(f2776,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| eqangle(X0,X1,X2,X0,X1,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2763,f138]) ).
fof(f2794,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| eqangle(X0,X1,X2,X1,X3,X0,X2,X3) ),
inference(resolution,[status(thm)],[f2776,f142]) ).
fof(f2795,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| eqangle(X0,X1,X1,X2,X0,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2776,f140]) ).
fof(f2826,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| eqangle(X0,X1,X2,X0,X3,X1,X2,X3) ),
inference(resolution,[status(thm)],[f2794,f138]) ).
fof(f2836,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| eqangle(X0,X1,X0,X2,X1,X3,X2,X3) ),
inference(resolution,[status(thm)],[f2795,f138]) ).
fof(f3025,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ7_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f2756,f2746]) ).
fof(f3027,plain,
! [X0,X1] :
( ~ sQ7_spl
| cong(X0,X0,X1,X1) ),
inference(resolution,[status(thm)],[f3025,f2836]) ).
fof(f3028,plain,
! [X0,X1] :
( ~ sQ7_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3025,f2826]) ).
fof(f3052,plain,
! [X0] :
( ~ sQ7_spl
| midp(X0,X0,X0) ),
inference(resolution,[status(thm)],[f3027,f2492]) ).
fof(f3062,plain,
! [X0,X1] :
( ~ sQ7_spl
| midp(X0,X1,X1) ),
inference(resolution,[status(thm)],[f3052,f2371]) ).
fof(f3067,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f3028,f232]) ).
fof(f3074,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f3067,f3028]) ).
fof(f3078,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| $false ),
inference(resolution,[status(thm)],[f3074,f1713]) ).
fof(f3084,plain,
( ~ sQ5_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f3078]) ).
fof(f3086,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ sQ7_spl
| cong(X0,X1,X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2144,f3062]) ).
fof(f3149,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| ~ sQ7_spl
| perp(X0,X2,X3,X1)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f232,f3086]) ).
fof(f3157,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| ~ sQ7_spl
| perp(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3149,f3086]) ).
fof(f3159,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| ~ sQ7_spl
| para(X4,X5,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f3157]) ).
fof(f3164,plain,
! [X0,X1,X2,X3] :
( ~ sQ4_spl
| ~ sQ7_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f3159,f3157]) ).
fof(f3200,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| ~ sQ7_spl
| eqangle(X0,X1,X2,X3,X0,X1,X4,X5) ),
inference(backward_subsumption_resolution,[status(thm)],[f1454,f3164]) ).
fof(f3202,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| ~ sQ7_spl
| eqangle(X0,X1,X2,X3,X4,X5,X4,X5) ),
inference(backward_subsumption_resolution,[status(thm)],[f1452,f3164]) ).
fof(f3294,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ4_spl
| ~ sQ7_spl
| eqangle(X0,X1,X0,X1,X2,X3,X4,X5) ),
inference(resolution,[status(thm)],[f3200,f144]) ).
fof(f3384,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ sQ4_spl
| ~ sQ7_spl
| eqangle(X0,X1,X2,X3,X6,X7,X8,X9)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X4,X5) ),
inference(resolution,[status(thm)],[f3294,f147]) ).
fof(f3389,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ4_spl
| ~ sQ7_spl
| eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(forward_subsumption_resolution,[status(thm)],[f3384,f3202]) ).
fof(f3551,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f376,f3389]) ).
fof(f3552,plain,
( ~ sQ4_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f3551]) ).
fof(f3553,plain,
$false,
inference(sat_refutation,[status(thm)],[f1715,f1824,f1876,f3084,f3552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO597+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 20 17:42:49 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 1.62/0.67 % Refutation found
% 1.62/0.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.62/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.62/0.69 % Elapsed time: 0.337770 seconds
% 1.62/0.69 % CPU time: 2.381780 seconds
% 1.62/0.69 % Total memory used: 109.522 MB
% 1.62/0.69 % Net memory used: 106.386 MB
%------------------------------------------------------------------------------