%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO610+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 : 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 12:25:22 PM UTC 2026
% Result : Theorem 14.26s 2.23s
% Output : CNFRefutation 14.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 34
% Syntax : Number of formulae : 188 ( 48 unt; 4 def)
% Number of atoms : 518 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 535 ( 205 ~; 207 |; 88 &)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 829 ( 805 !; 24 ?)
% 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(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(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(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(f46,axiom,
! [A,B,C,E,F] :
( ( coll(F,A,C)
& para(E,F,B,C)
& midp(E,A,B) )
=> midp(F,A,C) ),
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(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(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(f95,conjecture,
! [A,B,C,D,E,F,G,NWPNT1] :
( ( coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) )
=> ( eqangle(E,F,F,G,E,C,C,B)
& ( eqangle(F,E,E,G,E,B,B,C)
| eqangle(E,F,F,G,C,E,E,B) )
& ( eqangle(F,E,E,G,E,B,B,C)
| eqangle(E,F,F,G,E,B,B,C) )
& ( eqangle(F,E,E,G,E,C,C,B)
| eqangle(E,F,F,G,C,E,E,B) )
& ( eqangle(F,E,E,G,E,C,C,B)
| eqangle(E,F,F,G,E,B,B,C) )
& ( eqangle(F,E,E,G,C,E,E,B)
| eqangle(E,F,F,G,E,C,C,B) )
& eqangle(F,E,E,G,C,E,E,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,NWPNT1] :
( ( coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) )
=> ( eqangle(E,F,F,G,E,C,C,B)
& ( eqangle(F,E,E,G,E,B,B,C)
| eqangle(E,F,F,G,C,E,E,B) )
& ( eqangle(F,E,E,G,E,B,B,C)
| eqangle(E,F,F,G,E,B,B,C) )
& ( eqangle(F,E,E,G,E,C,C,B)
| eqangle(E,F,F,G,C,E,E,B) )
& ( eqangle(F,E,E,G,E,C,C,B)
| eqangle(E,F,F,G,E,B,B,C) )
& ( eqangle(F,E,E,G,C,E,E,B)
| eqangle(E,F,F,G,E,C,C,B) )
& eqangle(F,E,E,G,C,E,E,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(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(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(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(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(f202,plain,
! [A,B,C,E,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ~ para(E,F,B,C)
| ~ midp(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f203,plain,
! [A,C,F] :
( midp(F,A,C)
| ~ coll(F,A,C)
| ! [B,E] :
( ~ para(E,F,B,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ coll(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
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(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(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(f369,plain,
? [A,B,C,D,E,F,G,NWPNT1] :
( ( ~ eqangle(E,F,F,G,E,C,C,B)
| ( ~ eqangle(F,E,E,G,E,B,B,C)
& ~ eqangle(E,F,F,G,C,E,E,B) )
| ( ~ eqangle(F,E,E,G,E,B,B,C)
& ~ eqangle(E,F,F,G,E,B,B,C) )
| ( ~ eqangle(F,E,E,G,E,C,C,B)
& ~ eqangle(E,F,F,G,C,E,E,B) )
| ( ~ eqangle(F,E,E,G,E,C,C,B)
& ~ eqangle(E,F,F,G,E,B,B,C) )
| ( ~ eqangle(F,E,E,G,C,E,E,B)
& ~ eqangle(E,F,F,G,E,C,C,B) )
| ~ eqangle(F,E,E,G,C,E,E,B) )
& coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,definition,
! [B,C,E,F,G] :
( sP0_prd(G,F,E,C,B)
<=> ( ~ eqangle(F,E,E,G,C,E,E,B)
& ~ eqangle(E,F,F,G,E,C,C,B) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f371,definition,
! [B,C,E,F,G] :
( sP1_prd(G,F,E,C,B)
<=> ( ~ eqangle(F,E,E,G,E,C,C,B)
& ~ eqangle(E,F,F,G,E,B,B,C) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f372,definition,
! [B,C,E,F,G] :
( sP2_prd(G,F,E,C,B)
<=> ( ~ eqangle(F,E,E,G,E,C,C,B)
& ~ eqangle(E,F,F,G,C,E,E,B) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f373,definition,
! [B,C,E,F,G] :
( sP3_prd(G,F,E,C,B)
<=> ( ~ eqangle(F,E,E,G,E,B,B,C)
& ~ eqangle(E,F,F,G,E,B,B,C) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f374,plain,
? [A,B,C,D,E,F,G,NWPNT1] :
( ( ~ eqangle(E,F,F,G,E,C,C,B)
| ( ~ eqangle(F,E,E,G,E,B,B,C)
& ~ eqangle(E,F,F,G,C,E,E,B) )
| sP3_prd(G,F,E,C,B)
| sP2_prd(G,F,E,C,B)
| sP1_prd(G,F,E,C,B)
| sP0_prd(G,F,E,C,B)
| ~ eqangle(F,E,E,G,C,E,E,B) )
& coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) ),
inference(formula_renaming,[status(thm)],[f369,f373,f372,f371,f370]) ).
fof(f375,plain,
? [B,C,E,F,G] :
( ( ~ eqangle(E,F,F,G,E,C,C,B)
| ( ~ eqangle(F,E,E,G,E,B,B,C)
& ~ eqangle(E,F,F,G,C,E,E,B) )
| sP3_prd(G,F,E,C,B)
| sP2_prd(G,F,E,C,B)
| sP1_prd(G,F,E,C,B)
| sP0_prd(G,F,E,C,B)
| ~ eqangle(F,E,E,G,C,E,E,B) )
& ? [A] :
( coll(G,A,B)
& perp(G,E,A,B)
& coll(F,A,C)
& perp(F,E,A,C)
& ? [D] :
( ? [NWPNT1] : circle(D,A,E,NWPNT1)
& circle(D,A,B,C) ) ) ),
inference(miniscoping,[status(thm)],[f374]) ).
fof(f376,plain,
( ( ~ eqangle(sK22_skl,sK23_skl,sK23_skl,sK24_skl,sK22_skl,sK21_skl,sK21_skl,sK20_skl)
| ( ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK22_skl,sK20_skl,sK20_skl,sK21_skl)
& ~ eqangle(sK22_skl,sK23_skl,sK23_skl,sK24_skl,sK21_skl,sK22_skl,sK22_skl,sK20_skl) )
| sP3_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| sP1_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| sP0_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK21_skl,sK22_skl,sK22_skl,sK20_skl) )
& coll(sK24_skl,sK25_skl,sK20_skl)
& perp(sK24_skl,sK22_skl,sK25_skl,sK20_skl)
& coll(sK23_skl,sK25_skl,sK21_skl)
& perp(sK23_skl,sK22_skl,sK25_skl,sK21_skl)
& circle(sK26_skl,sK25_skl,sK22_skl,sK27_skl)
& circle(sK26_skl,sK25_skl,sK20_skl,sK21_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl]),skolemize(B,sK20_skl),skolemize(C,sK21_skl),skolemize(E,sK22_skl),skolemize(F,sK23_skl),skolemize(G,sK24_skl),skolemize(A,sK25_skl),skolemize(D,sK26_skl),skolemize(NWPNT1,sK27_skl)],[f375]) ).
fof(f381,plain,
perp(sK24_skl,sK22_skl,sK25_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f384,plain,
( ~ eqangle(sK22_skl,sK23_skl,sK23_skl,sK24_skl,sK22_skl,sK21_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK22_skl,sK20_skl,sK20_skl,sK21_skl)
| sP3_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| sP1_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| sP0_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK21_skl,sK22_skl,sK22_skl,sK20_skl) ),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f385,plain,
! [B,C,E,F,G] :
( ( eqangle(F,E,E,G,C,E,E,B)
| eqangle(E,F,F,G,E,C,C,B)
| sP0_prd(G,F,E,C,B) )
& ( ( ~ eqangle(F,E,E,G,C,E,E,B)
& ~ eqangle(E,F,F,G,E,C,C,B) )
| ~ sP0_prd(G,F,E,C,B) ) ),
inference(NNF_transformation,[status(thm)],[f370]) ).
fof(f386,plain,
( ! [B,C,E,F,G] :
( eqangle(F,E,E,G,C,E,E,B)
| eqangle(E,F,F,G,E,C,C,B)
| sP0_prd(G,F,E,C,B) )
& ! [B,C,E,F,G] :
( ( ~ eqangle(F,E,E,G,C,E,E,B)
& ~ eqangle(E,F,F,G,E,C,C,B) )
| ~ sP0_prd(G,F,E,C,B) ) ),
inference(miniscoping,[status(thm)],[f385]) ).
fof(f387,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X2,X1,X1,X0,X2,X3,X3,X4)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
fof(f390,plain,
! [B,C,E,F,G] :
( ( eqangle(F,E,E,G,E,C,C,B)
| eqangle(E,F,F,G,E,B,B,C)
| sP1_prd(G,F,E,C,B) )
& ( ( ~ eqangle(F,E,E,G,E,C,C,B)
& ~ eqangle(E,F,F,G,E,B,B,C) )
| ~ sP1_prd(G,F,E,C,B) ) ),
inference(NNF_transformation,[status(thm)],[f371]) ).
fof(f391,plain,
( ! [B,C,E,F,G] :
( eqangle(F,E,E,G,E,C,C,B)
| eqangle(E,F,F,G,E,B,B,C)
| sP1_prd(G,F,E,C,B) )
& ! [B,C,E,F,G] :
( ( ~ eqangle(F,E,E,G,E,C,C,B)
& ~ eqangle(E,F,F,G,E,B,B,C) )
| ~ sP1_prd(G,F,E,C,B) ) ),
inference(miniscoping,[status(thm)],[f390]) ).
fof(f392,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X2,X1,X1,X0,X2,X4,X4,X3)
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f391]) ).
fof(f395,plain,
! [B,C,E,F,G] :
( ( eqangle(F,E,E,G,E,C,C,B)
| eqangle(E,F,F,G,C,E,E,B)
| sP2_prd(G,F,E,C,B) )
& ( ( ~ eqangle(F,E,E,G,E,C,C,B)
& ~ eqangle(E,F,F,G,C,E,E,B) )
| ~ sP2_prd(G,F,E,C,B) ) ),
inference(NNF_transformation,[status(thm)],[f372]) ).
fof(f396,plain,
( ! [B,C,E,F,G] :
( eqangle(F,E,E,G,E,C,C,B)
| eqangle(E,F,F,G,C,E,E,B)
| sP2_prd(G,F,E,C,B) )
& ! [B,C,E,F,G] :
( ( ~ eqangle(F,E,E,G,E,C,C,B)
& ~ eqangle(E,F,F,G,C,E,E,B) )
| ~ sP2_prd(G,F,E,C,B) ) ),
inference(miniscoping,[status(thm)],[f395]) ).
fof(f398,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X1,X2,X2,X0,X2,X3,X3,X4)
| ~ sP2_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f396]) ).
fof(f400,plain,
! [B,C,E,F,G] :
( ( eqangle(F,E,E,G,E,B,B,C)
| eqangle(E,F,F,G,E,B,B,C)
| sP3_prd(G,F,E,C,B) )
& ( ( ~ eqangle(F,E,E,G,E,B,B,C)
& ~ eqangle(E,F,F,G,E,B,B,C) )
| ~ sP3_prd(G,F,E,C,B) ) ),
inference(NNF_transformation,[status(thm)],[f373]) ).
fof(f401,plain,
( ! [B,C,E,F,G] :
( eqangle(F,E,E,G,E,B,B,C)
| eqangle(E,F,F,G,E,B,B,C)
| sP3_prd(G,F,E,C,B) )
& ! [B,C,E,F,G] :
( ( ~ eqangle(F,E,E,G,E,B,B,C)
& ~ eqangle(E,F,F,G,E,B,B,C) )
| ~ sP3_prd(G,F,E,C,B) ) ),
inference(miniscoping,[status(thm)],[f400]) ).
fof(f403,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X1,X2,X2,X0,X2,X4,X4,X3)
| ~ sP3_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f401]) ).
fof(f446,plain,
perp(sK25_skl,sK20_skl,sK24_skl,sK22_skl),
inference(resolution,[status(thm)],[f114,f381]) ).
fof(f452,plain,
perp(sK25_skl,sK20_skl,sK22_skl,sK24_skl),
inference(resolution,[status(thm)],[f446,f112]) ).
fof(f471,plain,
! [X0,X1] :
( para(sK24_skl,sK22_skl,X0,X1)
| ~ perp(sK25_skl,sK20_skl,X0,X1) ),
inference(resolution,[status(thm)],[f117,f381]) ).
fof(f573,plain,
( ~ eqangle(sK22_skl,sK23_skl,sK23_skl,sK24_skl,sK22_skl,sK21_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK22_skl,sK20_skl,sK20_skl,sK21_skl)
| sP3_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| sP1_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK21_skl,sK22_skl,sK22_skl,sK20_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f384,f387]) ).
fof(f1789,plain,
( ~ eqangle(sK22_skl,sK23_skl,sK23_skl,sK24_skl,sK22_skl,sK21_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK22_skl,sK20_skl,sK20_skl,sK21_skl)
| sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| sP1_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK21_skl,sK22_skl,sK22_skl,sK20_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f403]) ).
fof(f1820,plain,
para(sK24_skl,sK22_skl,sK22_skl,sK24_skl),
inference(resolution,[status(thm)],[f471,f452]) ).
fof(f1821,plain,
para(sK24_skl,sK22_skl,sK24_skl,sK22_skl),
inference(resolution,[status(thm)],[f471,f446]) ).
fof(f1825,plain,
para(sK22_skl,sK24_skl,sK24_skl,sK22_skl),
inference(resolution,[status(thm)],[f1820,f107]) ).
fof(f1827,plain,
! [X0,X1] : eqangle(sK24_skl,sK22_skl,X0,X1,sK24_skl,sK22_skl,X0,X1),
inference(resolution,[status(thm)],[f1821,f189]) ).
fof(f1846,plain,
para(sK22_skl,sK24_skl,sK22_skl,sK24_skl),
inference(resolution,[status(thm)],[f1825,f105]) ).
fof(f1852,plain,
coll(sK22_skl,sK24_skl,sK24_skl),
inference(resolution,[status(thm)],[f1846,f256]) ).
fof(f1854,plain,
coll(sK24_skl,sK22_skl,sK24_skl),
inference(resolution,[status(thm)],[f1852,f100]) ).
fof(f1858,plain,
coll(sK24_skl,sK24_skl,sK22_skl),
inference(resolution,[status(thm)],[f1854,f98]) ).
fof(f2655,plain,
! [X0,X1] : eqangle(X0,X1,sK24_skl,sK22_skl,X0,X1,sK24_skl,sK22_skl),
inference(resolution,[status(thm)],[f1827,f140]) ).
fof(f4490,plain,
! [X0] :
( cyclic(X0,sK22_skl,sK24_skl,sK24_skl)
| ~ coll(sK24_skl,sK24_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f2655,f195]) ).
fof(f4494,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f2655,f186]) ).
fof(f4509,plain,
! [X0] : cyclic(X0,sK22_skl,sK24_skl,sK24_skl),
inference(forward_subsumption_resolution,[status(thm)],[f4490,f1858]) ).
fof(f4517,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f4494,f256]) ).
fof(f4720,plain,
! [X0,X1] : coll(X0,X1,X0),
inference(resolution,[status(thm)],[f4517,f100]) ).
fof(f4898,plain,
! [X0,X1] : coll(X0,X0,X1),
inference(resolution,[status(thm)],[f4720,f98]) ).
fof(f5016,plain,
! [X0,X1,X2] :
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f4898,f103]) ).
fof(f5019,plain,
! [X0,X1,X2] : coll(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f5016,f4898]) ).
fof(f5021,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f5019]) ).
fof(f5023,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ para(X0,X3,X2,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f5019]) ).
fof(f5038,plain,
! [X0] : cyclic(sK22_skl,X0,sK24_skl,sK24_skl),
inference(resolution,[status(thm)],[f4509,f133]) ).
fof(f5044,plain,
! [X0] : cyclic(sK22_skl,sK24_skl,X0,sK24_skl),
inference(resolution,[status(thm)],[f5038,f131]) ).
fof(f5055,plain,
! [X0] : cyclic(sK22_skl,sK24_skl,sK24_skl,X0),
inference(resolution,[status(thm)],[f5044,f129]) ).
fof(f5072,plain,
! [X0,X1] :
( cyclic(sK24_skl,sK24_skl,X1,X0)
| ~ cyclic(sK22_skl,sK24_skl,sK24_skl,X0) ),
inference(resolution,[status(thm)],[f5055,f136]) ).
fof(f5076,plain,
! [X0,X1] : cyclic(sK24_skl,sK24_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f5072,f5055]) ).
fof(f5078,plain,
! [X0,X1,X2] :
( cyclic(sK24_skl,X0,X2,X1)
| ~ cyclic(sK24_skl,sK24_skl,X0,X1) ),
inference(resolution,[status(thm)],[f5076,f136]) ).
fof(f5082,plain,
! [X0,X1,X2] : cyclic(sK24_skl,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f5078,f5076]) ).
fof(f5084,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(sK24_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f5082,f136]) ).
fof(f5088,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f5084,f5082]) ).
fof(f5091,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f198,f5088]) ).
fof(f5092,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
inference(backward_subsumption_resolution,[status(thm)],[f191,f5088]) ).
fof(f5093,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X5,X3)
| ~ eqangle(X2,X0,X2,X1,X4,X5,X4,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f5091,f5088]) ).
fof(f5261,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X1,X2,X3,X0,X3,X2),
inference(resolution,[status(thm)],[f5092,f138]) ).
fof(f5449,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X1,X2,X4,X5)
| ~ eqangle(X0,X1,X0,X2,X3,X4,X3,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f5093,f5088]) ).
fof(f5450,plain,
! [X0,X1] : cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f5449,f5261]) ).
fof(f5519,plain,
! [X0,X1] : midp(X0,X1,X1),
inference(resolution,[status(thm)],[f5450,f5021]) ).
fof(f5521,plain,
! [X0,X1,X2] :
( perp(X0,X0,X2,X1)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f5450,f232]) ).
fof(f5527,plain,
! [X0,X1,X2] : perp(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f5521,f5450]) ).
fof(f5563,plain,
! [X0,X1,X2] : perp(X0,X1,X2,X2),
inference(resolution,[status(thm)],[f5527,f114]) ).
fof(f5595,plain,
! [X0,X1,X2,X3,X4] :
( para(X3,X4,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f5563,f117]) ).
fof(f5598,plain,
! [X0,X1,X2,X3] : para(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f5595,f5527]) ).
fof(f5605,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f5023,f5598]) ).
fof(f5609,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3),
inference(backward_subsumption_resolution,[status(thm)],[f189,f5598]) ).
fof(f5615,plain,
! [X0,X1,X2] : midp(X0,X1,X2),
inference(resolution,[status(thm)],[f5605,f5519]) ).
fof(f5618,plain,
! [X0,X1,X2,X3,X4] :
( eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f216,f5615]) ).
fof(f5622,plain,
! [X0,X1,X2] : cong(X0,X1,X0,X2),
inference(backward_subsumption_resolution,[status(thm)],[f260,f5615]) ).
fof(f5632,plain,
! [X0,X1,X2,X3] :
( circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f124,f5622]) ).
fof(f5637,plain,
! [X0,X1,X2,X3] : circle(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f5632,f5622]) ).
fof(f5802,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5),
inference(resolution,[status(thm)],[f5609,f144]) ).
fof(f5957,plain,
! [X0,X1,X2,X3,X4] : eqangle(X0,X1,X0,X2,X3,X1,X3,X4),
inference(forward_subsumption_resolution,[status(thm)],[f5618,f5637]) ).
fof(f5974,plain,
! [X0,X1,X2,X3,X4] : eqangle(X0,X1,X1,X2,X3,X0,X3,X4),
inference(resolution,[status(thm)],[f5957,f138]) ).
fof(f6129,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X0,X1,X2,X3,X4,X5),
inference(resolution,[status(thm)],[f5802,f142]) ).
fof(f6447,plain,
! [X0,X1,X2,X3,X4] : eqangle(X0,X1,X0,X2,X1,X3,X3,X4),
inference(resolution,[status(thm)],[f5974,f142]) ).
fof(f6616,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X1,X0,X2,X3,X4,X5),
inference(resolution,[status(thm)],[f6129,f138]) ).
fof(f7207,plain,
! [X0,X1,X2,X3,X4] : eqangle(X0,X1,X1,X2,X0,X3,X3,X4),
inference(resolution,[status(thm)],[f6447,f138]) ).
fof(f7509,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X5,X4),
inference(resolution,[status(thm)],[f6616,f142]) ).
fof(f8315,plain,
( ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK22_skl,sK20_skl,sK20_skl,sK21_skl)
| sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| sP1_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK21_skl,sK22_skl,sK22_skl,sK20_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f1789,f7207]) ).
fof(f8317,plain,
! [X0,X1,X2,X3,X4] : ~ sP1_prd(X0,X1,X2,X3,X4),
inference(backward_subsumption_resolution,[status(thm)],[f392,f7207]) ).
fof(f8376,plain,
( ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK22_skl,sK20_skl,sK20_skl,sK21_skl)
| sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK21_skl,sK22_skl,sK22_skl,sK20_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f8315,f8317]) ).
fof(f8444,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( eqangle(X6,X7,X8,X9,X2,X3,X4,X5)
| ~ eqangle(X0,X1,X1,X0,X2,X3,X4,X5) ),
inference(resolution,[status(thm)],[f7509,f147]) ).
fof(f8449,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : eqangle(X0,X1,X2,X3,X4,X5,X6,X7),
inference(forward_subsumption_resolution,[status(thm)],[f8444,f6616]) ).
fof(f9001,plain,
( sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK23_skl,sK22_skl,sK22_skl,sK24_skl,sK21_skl,sK22_skl,sK22_skl,sK20_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f8376,f8449]) ).
fof(f9003,plain,
! [X0,X1,X2,X3,X4] : ~ sP2_prd(X0,X1,X2,X3,X4),
inference(backward_subsumption_resolution,[status(thm)],[f398,f8449]) ).
fof(f9005,plain,
sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl),
inference(forward_subsumption_resolution,[status(thm)],[f9001,f8449]) ).
fof(f9032,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f9005,f9003]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO610+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 17:50:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 14.26/2.23 % Refutation found
% 14.26/2.23 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.26/2.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.26/2.25 % Elapsed time: 1.892146 seconds
% 14.26/2.25 % CPU time: 14.597080 seconds
% 14.26/2.25 % Total memory used: 157.626 MB
% 14.26/2.25 % Net memory used: 145.601 MB
%------------------------------------------------------------------------------