%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO613+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 : n001.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 12:25:22 PM UTC 2026
% Result : Theorem 7.90s 6.50s
% Output : CNFRefutation 6.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 47
% Syntax : Number of formulae : 264 ( 6 unt; 5 def)
% Number of atoms : 760 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 876 ( 380 ~; 377 |; 71 &)
% ( 5 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 6 prp; 0-8 aty)
% Number of functors : 16 ( 16 usr; 16 con; 0-0 aty)
% Number of variables : 1004 ( 972 !; 32 ?)
% 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(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
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(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
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(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
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(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/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(f25,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
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(f42,axiom,
! [A,B,P,Q] :
( ( ~ coll(P,Q,A)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
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(f45,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
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(f51,axiom,
! [A,B,C,O,M] :
( ( midp(M,B,C)
& circle(O,A,B,C) )
=> eqangle(A,B,A,C,O,B,O,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A,B,M,O] :
( ( perp(O,M,A,B)
& midp(M,A,B) )
=> cong(O,A,O,B) ),
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(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/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(f68,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(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(f70,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,conjecture,
! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ( coll(H,C,G)
& coll(H,A,F)
& coll(G,B,F)
& circle(C,B,G,NWPNT8)
& circle(A,B,F,NWPNT7)
& midp(E,D,B)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) )
=> eqangle(F,D,D,G,A,H,H,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ( coll(H,C,G)
& coll(H,A,F)
& coll(G,B,F)
& circle(C,B,G,NWPNT8)
& circle(A,B,F,NWPNT7)
& midp(E,D,B)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) )
=> eqangle(F,D,D,G,A,H,H,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(f104,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
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(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(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(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(f123,plain,
! [A,B,C,O] :
( circle(O,A,B,C)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
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(f128,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f132,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
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(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(f152,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f153,plain,
! [A,B,E,F] :
( cong(A,B,E,F)
| ! [C,D] :
( ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
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(f192,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| coll(P,Q,A)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f193,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| coll(X0,X3,X1)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
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(f199,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f200,plain,
! [B,C,E,F] :
( para(E,F,B,C)
| ! [A] :
( ~ midp(F,A,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f199]) ).
fof(f201,plain,
! [X0,X1,X2,X3,X4] :
( para(X0,X3,X2,X4)
| ~ midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
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(f215,plain,
! [A,B,C,O,M] :
( eqangle(A,B,A,C,O,B,O,M)
| ~ midp(M,B,C)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f216,plain,
! [X0,X1,X2,X3,X4] :
( eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ midp(X4,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f228,plain,
! [A,B,M,O] :
( cong(O,A,O,B)
| ~ perp(O,M,A,B)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f229,plain,
! [A,B,O] :
( cong(O,A,O,B)
| ! [M] :
( ~ perp(O,M,A,B)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f228]) ).
fof(f230,plain,
! [X0,X1,X2,X3] :
( cong(X3,X1,X3,X2)
| ~ perp(X3,X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f229]) ).
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(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(f261,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f70]) ).
fof(f262,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f369,plain,
? [A,B,C,D,E,F,G,H,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8] :
( ~ eqangle(F,D,D,G,A,H,H,C)
& coll(H,C,G)
& coll(H,A,F)
& coll(G,B,F)
& circle(C,B,G,NWPNT8)
& circle(A,B,F,NWPNT7)
& midp(E,D,B)
& circle(C,B,D,NWPNT6)
& circle(A,B,D,NWPNT5)
& circle(C,B,NWPNT3,NWPNT4)
& circle(A,B,NWPNT1,NWPNT2) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,plain,
? [A,C,D,F,G,H] :
( ~ eqangle(F,D,D,G,A,H,H,C)
& coll(H,C,G)
& coll(H,A,F)
& ? [B] :
( coll(G,B,F)
& ? [NWPNT8] : circle(C,B,G,NWPNT8)
& ? [NWPNT7] : circle(A,B,F,NWPNT7)
& ? [E] : midp(E,D,B)
& ? [NWPNT6] : circle(C,B,D,NWPNT6)
& ? [NWPNT5] : circle(A,B,D,NWPNT5)
& ? [NWPNT3,NWPNT4] : circle(C,B,NWPNT3,NWPNT4)
& ? [NWPNT1,NWPNT2] : circle(A,B,NWPNT1,NWPNT2) ) ),
inference(miniscoping,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK20_skl,sK25_skl,sK25_skl,sK21_skl)
& coll(sK25_skl,sK21_skl,sK24_skl)
& coll(sK25_skl,sK20_skl,sK23_skl)
& coll(sK24_skl,sK26_skl,sK23_skl)
& circle(sK21_skl,sK26_skl,sK24_skl,sK35_skl)
& circle(sK20_skl,sK26_skl,sK23_skl,sK34_skl)
& midp(sK33_skl,sK22_skl,sK26_skl)
& circle(sK21_skl,sK26_skl,sK22_skl,sK32_skl)
& circle(sK20_skl,sK26_skl,sK22_skl,sK31_skl)
& circle(sK21_skl,sK26_skl,sK29_skl,sK30_skl)
& circle(sK20_skl,sK26_skl,sK27_skl,sK28_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(C,sK21_skl),skolemize(D,sK22_skl),skolemize(F,sK23_skl),skolemize(G,sK24_skl),skolemize(H,sK25_skl),skolemize(B,sK26_skl),skolemize(NWPNT1,sK27_skl),skolemize(NWPNT2,sK28_skl),skolemize(NWPNT3,sK29_skl),skolemize(NWPNT4,sK30_skl),skolemize(NWPNT5,sK31_skl),skolemize(NWPNT6,sK32_skl),skolemize(E,sK33_skl),skolemize(NWPNT7,sK34_skl),skolemize(NWPNT8,sK35_skl)],[f370]) ).
fof(f376,plain,
midp(sK33_skl,sK22_skl,sK26_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f382,plain,
~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK20_skl,sK25_skl,sK25_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f386,plain,
~ eqangle(sK22_skl,sK23_skl,sK22_skl,sK24_skl,sK20_skl,sK25_skl,sK25_skl,sK21_skl),
inference(resolution,[status(thm)],[f382,f138]) ).
fof(f388,plain,
! [X0,X1,X2] :
( ~ cong(X0,X2,X0,X1)
| midp(X0,X1,X2)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f258,f151]) ).
fof(f392,plain,
! [X0,X1,X2] :
( ~ cong(X0,X2,X1,X0)
| midp(X0,X1,X2)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f388,f149]) ).
fof(f399,plain,
! [X0,X1,X2] :
( ~ cong(X1,X0,X0,X2)
| midp(X0,X1,X2)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f392,f151]) ).
fof(f406,plain,
! [X0,X1,X2] :
( ~ cong(X1,X0,X2,X0)
| midp(X0,X1,X2)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f399,f149]) ).
fof(f423,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X2,X3,X4,X5,X0,X1,X4,X5)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f186,f142]) ).
fof(f424,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)],[f186,f140]) ).
fof(f426,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X1,X0,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f186,f138]) ).
fof(f455,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(f470,plain,
! [X0,X1,X2,X3] :
( ~ eqangle(X0,X1,X2,X3,sK20_skl,sK25_skl,sK25_skl,sK21_skl)
| ~ eqangle(sK22_skl,sK23_skl,sK22_skl,sK24_skl,X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f147,f386]) ).
fof(f481,definition,
( sQ0_spl
<=> cong(sK22_skl,sK33_skl,sK26_skl,sK33_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ0_spl
| cong(sK22_skl,sK33_skl,sK26_skl,sK33_skl) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f483,plain,
( sQ0_spl
| ~ cong(sK22_skl,sK33_skl,sK26_skl,sK33_skl) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f490,definition,
( sQ2_spl
<=> coll(sK33_skl,sK22_skl,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ2_spl
| ~ coll(sK33_skl,sK22_skl,sK26_skl) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f497,definition,
( sQ4_spl
<=> coll(sK33_skl,sK26_skl,sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ4_spl
| coll(sK33_skl,sK26_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f499,plain,
( sQ4_spl
| ~ coll(sK33_skl,sK26_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f505,plain,
( sQ2_spl
| ~ midp(sK33_skl,sK22_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f492,f262]) ).
fof(f508,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f376]) ).
fof(f509,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f518,plain,
( sQ4_spl
| ~ coll(sK33_skl,sK22_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f499,f98]) ).
fof(f519,plain,
( sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f518,f490,f497]) ).
fof(f594,plain,
! [X0,X1] :
( ~ sQ0_spl
| cong(X0,X1,sK26_skl,sK33_skl)
| ~ cong(X0,X1,sK22_skl,sK33_skl) ),
inference(resolution,[status(thm)],[f154,f482]) ).
fof(f598,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ cong(sK22_skl,sK33_skl,X0,X1)
| cong(X0,X1,sK26_skl,sK33_skl) ),
inference(resolution,[status(thm)],[f594,f151]) ).
fof(f601,plain,
( ~ sQ0_spl
| cong(sK26_skl,sK33_skl,sK26_skl,sK33_skl) ),
inference(resolution,[status(thm)],[f598,f482]) ).
fof(f612,plain,
( ~ sQ0_spl
| midp(sK26_skl,sK33_skl,sK33_skl)
| ~ coll(sK26_skl,sK33_skl,sK33_skl) ),
inference(resolution,[status(thm)],[f601,f388]) ).
fof(f622,definition,
( sQ8_spl
<=> coll(sK26_skl,sK33_skl,sK33_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f624,plain,
( sQ8_spl
| ~ coll(sK26_skl,sK33_skl,sK33_skl) ),
inference(component_clause,[status(thm)],[f622]) ).
fof(f625,definition,
( sQ9_spl
<=> midp(sK26_skl,sK33_skl,sK33_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( ~ sQ9_spl
| midp(sK26_skl,sK33_skl,sK33_skl) ),
inference(component_clause,[status(thm)],[f625]) ).
fof(f628,plain,
( ~ sQ0_spl
| sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f612,f622,f625,f481]) ).
fof(f631,plain,
( sQ0_spl
| ~ cong(sK22_skl,sK33_skl,sK33_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f483,f149]) ).
fof(f639,plain,
( sQ0_spl
| ~ cong(sK33_skl,sK26_skl,sK22_skl,sK33_skl) ),
inference(resolution,[status(thm)],[f631,f151]) ).
fof(f644,plain,
( sQ0_spl
| ~ cong(sK33_skl,sK26_skl,sK33_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f639,f149]) ).
fof(f649,plain,
( sQ0_spl
| ~ midp(sK33_skl,sK26_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f644,f260]) ).
fof(f650,plain,
( sQ0_spl
| ~ midp(sK33_skl,sK22_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f649,f122]) ).
fof(f651,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f650,f376]) ).
fof(f652,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f651]) ).
fof(f660,plain,
( sQ8_spl
| ~ coll(sK33_skl,sK26_skl,sK33_skl) ),
inference(resolution,[status(thm)],[f624,f100]) ).
fof(f681,plain,
( sQ8_spl
| ~ coll(sK33_skl,sK33_skl,sK26_skl) ),
inference(resolution,[status(thm)],[f660,f98]) ).
fof(f695,plain,
! [X0] :
( sQ8_spl
| ~ coll(sK26_skl,X0,sK33_skl)
| ~ coll(sK26_skl,X0,sK33_skl) ),
inference(resolution,[status(thm)],[f681,f103]) ).
fof(f699,plain,
! [X0] :
( sQ8_spl
| ~ coll(sK26_skl,X0,sK33_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f695]) ).
fof(f703,plain,
! [X0] :
( sQ8_spl
| ~ coll(sK26_skl,sK33_skl,X0) ),
inference(resolution,[status(thm)],[f699,f98]) ).
fof(f711,plain,
! [X0] :
( sQ8_spl
| ~ coll(sK33_skl,sK26_skl,X0) ),
inference(resolution,[status(thm)],[f703,f100]) ).
fof(f719,plain,
( ~ sQ4_spl
| sQ8_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f498,f711]) ).
fof(f724,plain,
( ~ sQ4_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f719]) ).
fof(f780,plain,
! [X0,X1,X2,X3] :
( ~ midp(X1,X3,X2)
| cong(X0,X2,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f230,f122]) ).
fof(f824,plain,
! [X0,X1,X2,X3] :
( ~ eqangle(X0,X2,X1,X2,X0,X3,X1,X3)
| cyclic(X2,X3,X0,X1)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f193,f144]) ).
fof(f864,plain,
! [X0,X1] :
( ~ cong(X0,X0,X0,X1)
| para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[f423,f206]) ).
fof(f866,plain,
! [X0,X1] :
( ~ cong(X0,X1,X0,X0)
| para(X0,X1,X0,X0) ),
inference(resolution,[status(thm)],[f864,f151]) ).
fof(f890,plain,
! [X0,X1,X2] :
( ~ cyclic(X0,X2,X1,X1)
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f426,f191]) ).
fof(f906,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X2,X0,X3,X1)
| ~ cyclic(X2,X0,X3,X1)
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f890,f136]) ).
fof(f910,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X2,X0,X3,X1)
| para(X0,X1,X1,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f906]) ).
fof(f913,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X2,X3,X0,X1)
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f910,f131]) ).
fof(f926,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X2,X3,X1,X0)
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f913,f129]) ).
fof(f941,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X2,X1,X3,X0)
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f926,f131]) ).
fof(f952,plain,
! [X0,X1,X2,X3] :
( ~ cyclic(X1,X2,X3,X0)
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f941,f133]) ).
fof(f958,plain,
! [X0,X1,X2,X3] :
( ~ eqangle(X0,X3,X1,X3,X0,X2,X1,X2)
| cyclic(X3,X2,X0,X1)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f195,f144]) ).
fof(f1036,plain,
! [X0] :
( ~ sQ0_spl
| ~ midp(sK26_skl,sK33_skl,X0)
| cyclic(sK33_skl,sK33_skl,X0,X0) ),
inference(resolution,[status(thm)],[f455,f601]) ).
fof(f1108,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| cyclic(sK33_skl,sK33_skl,sK33_skl,sK33_skl) ),
inference(resolution,[status(thm)],[f1036,f626]) ).
fof(f1111,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| para(sK33_skl,sK33_skl,sK33_skl,sK33_skl) ),
inference(resolution,[status(thm)],[f1108,f952]) ).
fof(f1147,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| eqangle(sK33_skl,sK33_skl,X0,X1,sK33_skl,sK33_skl,X0,X1) ),
inference(resolution,[status(thm)],[f1111,f189]) ).
fof(f1169,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| para(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f1147,f424]) ).
fof(f1186,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| eqangle(X0,X1,X2,X3,X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1169,f189]) ).
fof(f1190,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| para(X0,X1,X1,X0) ),
inference(resolution,[status(thm)],[f1169,f105]) ).
fof(f1191,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f1169,f256]) ).
fof(f1207,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| eqangle(X0,X1,X2,X3,X1,X0,X2,X3) ),
inference(resolution,[status(thm)],[f1190,f189]) ).
fof(f1208,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| perp(X1,X0,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1190,f120]) ).
fof(f1258,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ perp(X1,X0,X3,X2)
| perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1208,f112]) ).
fof(f1267,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ perp(X3,X2,X1,X0)
| perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1258,f114]) ).
fof(f1273,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ perp(X3,X2,X0,X1)
| perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1267,f112]) ).
fof(f1491,plain,
! [X0,X1] :
( ~ sQ9_spl
| midp(sK26_skl,X0,X1)
| ~ para(sK33_skl,X1,sK33_skl,X0)
| ~ para(sK33_skl,X0,sK33_skl,X1) ),
inference(resolution,[status(thm)],[f252,f626]) ).
fof(f1496,plain,
! [X0,X1] :
( ~ sQ9_spl
| midp(sK26_skl,X1,X0)
| ~ para(sK33_skl,X0,sK33_skl,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1491,f107]) ).
fof(f1581,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(sK26_skl,X0,X0) ),
inference(resolution,[status(thm)],[f1496,f1169]) ).
fof(f1594,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(sK26_skl,X1,X2)
| ~ para(X0,X2,X0,X1)
| ~ para(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[f1581,f252]) ).
fof(f1598,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| para(X0,sK26_skl,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1581,f201]) ).
fof(f1607,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(sK26_skl,X2,X1)
| ~ para(X0,X1,X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1594,f107]) ).
fof(f2059,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(sK26_skl,X1,sK26_skl)
| ~ midp(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1598,f1607]) ).
fof(f2815,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| cyclic(X2,X2,X0,X1)
| coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f824,f1186]) ).
fof(f4102,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| cyclic(X2,X2,X0,X1)
| ~ coll(X0,X1,X2) ),
inference(resolution,[status(thm)],[f958,f1186]) ).
fof(f4112,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| cyclic(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4102,f2815]) ).
fof(f4129,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4112,f136]) ).
fof(f4134,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4129,f4112]) ).
fof(f4137,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f4134]) ).
fof(f4138,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ9_spl
| ~ sQ0_spl
| cong(X0,X1,X5,X3)
| ~ eqangle(X2,X0,X2,X1,X4,X5,X4,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f198,f4134]) ).
fof(f4141,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ9_spl
| ~ sQ0_spl
| cong(X0,X1,X4,X5)
| ~ eqangle(X2,X0,X2,X1,X3,X4,X3,X5)
| ~ cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4138,f4134]) ).
fof(f4365,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ9_spl
| ~ sQ0_spl
| cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f4141,f4134]) ).
fof(f4368,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4365,f1207]) ).
fof(f4382,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4368,f4137]) ).
fof(f4395,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| perp(X0,X0,X1,X2)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f4368,f232]) ).
fof(f4405,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(X0,X1,X1)
| ~ coll(X0,X1,X1) ),
inference(resolution,[status(thm)],[f4368,f406]) ).
fof(f4413,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| perp(X0,X1,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4382,f4368]) ).
fof(f4414,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| perp(X0,X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4395,f4368]) ).
fof(f4415,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(X0,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f4405,f1191]) ).
fof(f4434,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(sK26_skl,X0,sK26_skl) ),
inference(resolution,[status(thm)],[f4415,f2059]) ).
fof(f4566,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| cong(X0,sK26_skl,X0,X1)
| ~ perp(X0,sK26_skl,sK26_skl,X1) ),
inference(resolution,[status(thm)],[f4434,f780]) ).
fof(f4577,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| cong(X0,sK26_skl,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f4566,f4413]) ).
fof(f4604,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| para(X0,sK26_skl,X0,X0) ),
inference(resolution,[status(thm)],[f4577,f866]) ).
fof(f4657,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| perp(X0,sK26_skl,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4604,f120]) ).
fof(f4662,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| perp(X0,sK26_skl,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4657,f4414]) ).
fof(f4679,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| perp(X0,X1,sK26_skl,X2) ),
inference(resolution,[status(thm)],[f4662,f1273]) ).
fof(f4681,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| perp(sK26_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f4662,f1258]) ).
fof(f4730,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ9_spl
| ~ sQ0_spl
| para(X0,X1,X3,X4)
| ~ perp(X0,X1,sK26_skl,X2) ),
inference(resolution,[status(thm)],[f4681,f117]) ).
fof(f4731,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| para(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4730,f4679]) ).
fof(f4794,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(X0,X3,X4)
| ~ para(X1,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f252,f4731]) ).
fof(f4799,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(sK26_skl,X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1607,f4731]) ).
fof(f4800,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ9_spl
| ~ sQ0_spl
| eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f189,f4731]) ).
fof(f4806,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4794,f4731]) ).
fof(f4924,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| cong(X0,X1,X0,X2)
| ~ perp(X0,sK26_skl,X1,X2) ),
inference(resolution,[status(thm)],[f4799,f780]) ).
fof(f4927,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| cong(X0,X1,X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4924,f4662]) ).
fof(f4932,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f124,f4927]) ).
fof(f4943,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ0_spl
| circle(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f4932,f4927]) ).
fof(f4944,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ9_spl
| ~ sQ0_spl
| eqangle(X3,X1,X3,X2,X4,X1,X4,X0)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f216,f4943]) ).
fof(f5004,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ0_spl
| midp(X0,X1,X2) ),
inference(resolution,[status(thm)],[f4806,f4415]) ).
fof(f5042,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ eqangle(sK22_skl,sK23_skl,sK22_skl,sK24_skl,X0,X1,sK25_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f4800,f470]) ).
fof(f5095,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ9_spl
| ~ sQ0_spl
| eqangle(X0,X1,X0,X2,X3,X1,X3,X4) ),
inference(forward_subsumption_resolution,[status(thm)],[f4944,f5004]) ).
fof(f5159,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| $false ),
inference(resolution,[status(thm)],[f5042,f5095]) ).
fof(f5177,plain,
( ~ sQ9_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f5159]) ).
fof(f5178,plain,
$false,
inference(sat_refutation,[status(thm)],[f509,f519,f628,f652,f724,f5177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO613+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n001.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sun Sep 20 18:00:34 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.39 % Drodi V4.1.1
% 7.90/6.50 % Refutation found
% 7.90/6.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.90/6.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.08/6.54 % Elapsed time: 1.143146 seconds
% 6.08/6.54 % CPU time: 8.831555 seconds
% 6.08/6.54 % Total memory used: 163.715 MB
% 6.08/6.54 % Net memory used: 152.490 MB
%------------------------------------------------------------------------------