%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO599+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 : n013.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 17.14s 2.62s
% Output : CNFRefutation 14.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 33
% Syntax : Number of formulae : 195 ( 48 unt; 4 def)
% Number of atoms : 551 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 583 ( 227 ~; 230 |; 92 &)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 901 ( 871 !; 30 ?)
% 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(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(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(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(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(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(f53,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [A,B,P,Q] :
( ( cyclic(A,B,P,Q)
& cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(P,A,A,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,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(f95,conjecture,
! [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(F,A,G,NWPNT3)
& coll(G,B,C)
& circle(F,A,NWPNT1,NWPNT2)
& coll(F,D,E)
& midp(E,B,A)
& circle(D,A,B,C) )
=> ( eqangle(A,D,D,F,A,C,C,G)
& ( eqangle(D,A,A,F,A,G,G,C)
| eqangle(A,D,D,F,C,A,A,G) )
& ( eqangle(D,A,A,F,A,G,G,C)
| eqangle(A,D,D,F,A,G,G,C) )
& ( eqangle(D,A,A,F,A,C,C,G)
| eqangle(A,D,D,F,C,A,A,G) )
& ( eqangle(D,A,A,F,A,C,C,G)
| eqangle(A,D,D,F,A,G,G,C) )
& ( eqangle(D,A,A,F,C,A,A,G)
| eqangle(A,D,D,F,A,C,C,G) )
& eqangle(D,A,A,F,C,A,A,G) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,negated_conjecture,
~ ! [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3] :
( ( circle(F,A,G,NWPNT3)
& coll(G,B,C)
& circle(F,A,NWPNT1,NWPNT2)
& coll(F,D,E)
& midp(E,B,A)
& circle(D,A,B,C) )
=> ( eqangle(A,D,D,F,A,C,C,G)
& ( eqangle(D,A,A,F,A,G,G,C)
| eqangle(A,D,D,F,C,A,A,G) )
& ( eqangle(D,A,A,F,A,G,G,C)
| eqangle(A,D,D,F,A,G,G,C) )
& ( eqangle(D,A,A,F,A,C,C,G)
| eqangle(A,D,D,F,C,A,A,G) )
& ( eqangle(D,A,A,F,A,C,C,G)
| eqangle(A,D,D,F,A,G,G,C) )
& ( eqangle(D,A,A,F,C,A,A,G)
| eqangle(A,D,D,F,A,C,C,G) )
& eqangle(D,A,A,F,C,A,A,G) ) ),
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(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(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(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(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(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(f220,plain,
! [A,B,C,M] :
( cong(A,M,B,M)
| ~ midp(M,A,C)
| ~ perp(A,B,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f221,plain,
! [A,B,M] :
( cong(A,M,B,M)
| ! [C] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C) ) ),
inference(miniscoping,[status(thm)],[f220]) ).
fof(f222,plain,
! [X0,X1,X2,X3] :
( cong(X0,X3,X1,X3)
| ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f231,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f232,plain,
! [X0,X1,X2,X3] :
( perp(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f233,plain,
! [A,B,P,Q] :
( perp(P,A,A,Q)
| ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f234,plain,
! [A,P,Q] :
( perp(P,A,A,Q)
| ! [B] :
( ~ cyclic(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ) ),
inference(miniscoping,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cyclic(X0,X2,X1,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f247,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f248,plain,
! [A,B,C,D] :
( para(A,C,B,D)
| ! [M] :
( ~ midp(M,C,D)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f247]) ).
fof(f249,plain,
! [X0,X1,X2,X3,X4] :
( para(X1,X3,X2,X4)
| ~ midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
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(f369,plain,
? [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3] :
( ( ~ eqangle(A,D,D,F,A,C,C,G)
| ( ~ eqangle(D,A,A,F,A,G,G,C)
& ~ eqangle(A,D,D,F,C,A,A,G) )
| ( ~ eqangle(D,A,A,F,A,G,G,C)
& ~ eqangle(A,D,D,F,A,G,G,C) )
| ( ~ eqangle(D,A,A,F,A,C,C,G)
& ~ eqangle(A,D,D,F,C,A,A,G) )
| ( ~ eqangle(D,A,A,F,A,C,C,G)
& ~ eqangle(A,D,D,F,A,G,G,C) )
| ( ~ eqangle(D,A,A,F,C,A,A,G)
& ~ eqangle(A,D,D,F,A,C,C,G) )
| ~ eqangle(D,A,A,F,C,A,A,G) )
& circle(F,A,G,NWPNT3)
& coll(G,B,C)
& circle(F,A,NWPNT1,NWPNT2)
& coll(F,D,E)
& midp(E,B,A)
& circle(D,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f370,definition,
! [A,C,D,F,G] :
( sP0_prd(G,F,D,C,A)
<=> ( ~ eqangle(D,A,A,F,C,A,A,G)
& ~ eqangle(A,D,D,F,A,C,C,G) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f371,definition,
! [A,C,D,F,G] :
( sP1_prd(G,F,D,C,A)
<=> ( ~ eqangle(D,A,A,F,A,C,C,G)
& ~ eqangle(A,D,D,F,A,G,G,C) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f372,definition,
! [A,C,D,F,G] :
( sP2_prd(G,F,D,C,A)
<=> ( ~ eqangle(D,A,A,F,A,C,C,G)
& ~ eqangle(A,D,D,F,C,A,A,G) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f373,definition,
! [A,C,D,F,G] :
( sP3_prd(G,F,D,C,A)
<=> ( ~ eqangle(D,A,A,F,A,G,G,C)
& ~ eqangle(A,D,D,F,A,G,G,C) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f374,plain,
? [A,B,C,D,E,F,G,NWPNT1,NWPNT2,NWPNT3] :
( ( ~ eqangle(A,D,D,F,A,C,C,G)
| ( ~ eqangle(D,A,A,F,A,G,G,C)
& ~ eqangle(A,D,D,F,C,A,A,G) )
| sP3_prd(G,F,D,C,A)
| sP2_prd(G,F,D,C,A)
| sP1_prd(G,F,D,C,A)
| sP0_prd(G,F,D,C,A)
| ~ eqangle(D,A,A,F,C,A,A,G) )
& circle(F,A,G,NWPNT3)
& coll(G,B,C)
& circle(F,A,NWPNT1,NWPNT2)
& coll(F,D,E)
& midp(E,B,A)
& circle(D,A,B,C) ),
inference(formula_renaming,[status(thm)],[f369,f373,f372,f371,f370]) ).
fof(f375,plain,
? [A,C,D,F,G] :
( ( ~ eqangle(A,D,D,F,A,C,C,G)
| ( ~ eqangle(D,A,A,F,A,G,G,C)
& ~ eqangle(A,D,D,F,C,A,A,G) )
| sP3_prd(G,F,D,C,A)
| sP2_prd(G,F,D,C,A)
| sP1_prd(G,F,D,C,A)
| sP0_prd(G,F,D,C,A)
| ~ eqangle(D,A,A,F,C,A,A,G) )
& ? [NWPNT3] : circle(F,A,G,NWPNT3)
& ? [B] :
( coll(G,B,C)
& ? [NWPNT1,NWPNT2] : circle(F,A,NWPNT1,NWPNT2)
& ? [E] :
( coll(F,D,E)
& midp(E,B,A)
& circle(D,A,B,C) ) ) ),
inference(miniscoping,[status(thm)],[f374]) ).
fof(f376,plain,
( ( ~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK20_skl,sK21_skl,sK21_skl,sK24_skl)
| ( ~ eqangle(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK20_skl,sK24_skl,sK24_skl,sK21_skl)
& ~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK21_skl,sK20_skl,sK20_skl,sK24_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(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK21_skl,sK20_skl,sK20_skl,sK24_skl) )
& circle(sK23_skl,sK20_skl,sK24_skl,sK29_skl)
& coll(sK24_skl,sK25_skl,sK21_skl)
& circle(sK23_skl,sK20_skl,sK27_skl,sK28_skl)
& coll(sK23_skl,sK22_skl,sK26_skl)
& midp(sK26_skl,sK25_skl,sK20_skl)
& circle(sK22_skl,sK20_skl,sK25_skl,sK21_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl,sK29_skl]),skolemize(A,sK20_skl),skolemize(C,sK21_skl),skolemize(D,sK22_skl),skolemize(F,sK23_skl),skolemize(G,sK24_skl),skolemize(B,sK25_skl),skolemize(E,sK26_skl),skolemize(NWPNT1,sK27_skl),skolemize(NWPNT2,sK28_skl),skolemize(NWPNT3,sK29_skl)],[f375]) ).
fof(f378,plain,
midp(sK26_skl,sK25_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f384,plain,
( ~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK20_skl,sK21_skl,sK21_skl,sK24_skl)
| ~ eqangle(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK20_skl,sK24_skl,sK24_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(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK21_skl,sK20_skl,sK20_skl,sK24_skl) ),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f385,plain,
! [A,C,D,F,G] :
( ( eqangle(D,A,A,F,C,A,A,G)
| eqangle(A,D,D,F,A,C,C,G)
| sP0_prd(G,F,D,C,A) )
& ( ( ~ eqangle(D,A,A,F,C,A,A,G)
& ~ eqangle(A,D,D,F,A,C,C,G) )
| ~ sP0_prd(G,F,D,C,A) ) ),
inference(NNF_transformation,[status(thm)],[f370]) ).
fof(f386,plain,
( ! [A,C,D,F,G] :
( eqangle(D,A,A,F,C,A,A,G)
| eqangle(A,D,D,F,A,C,C,G)
| sP0_prd(G,F,D,C,A) )
& ! [A,C,D,F,G] :
( ( ~ eqangle(D,A,A,F,C,A,A,G)
& ~ eqangle(A,D,D,F,A,C,C,G) )
| ~ sP0_prd(G,F,D,C,A) ) ),
inference(miniscoping,[status(thm)],[f385]) ).
fof(f387,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X4,X2,X2,X1,X4,X3,X3,X0)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
fof(f390,plain,
! [A,C,D,F,G] :
( ( eqangle(D,A,A,F,A,C,C,G)
| eqangle(A,D,D,F,A,G,G,C)
| sP1_prd(G,F,D,C,A) )
& ( ( ~ eqangle(D,A,A,F,A,C,C,G)
& ~ eqangle(A,D,D,F,A,G,G,C) )
| ~ sP1_prd(G,F,D,C,A) ) ),
inference(NNF_transformation,[status(thm)],[f371]) ).
fof(f391,plain,
( ! [A,C,D,F,G] :
( eqangle(D,A,A,F,A,C,C,G)
| eqangle(A,D,D,F,A,G,G,C)
| sP1_prd(G,F,D,C,A) )
& ! [A,C,D,F,G] :
( ( ~ eqangle(D,A,A,F,A,C,C,G)
& ~ eqangle(A,D,D,F,A,G,G,C) )
| ~ sP1_prd(G,F,D,C,A) ) ),
inference(miniscoping,[status(thm)],[f390]) ).
fof(f392,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X4,X2,X2,X1,X4,X0,X0,X3)
| ~ sP1_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f391]) ).
fof(f395,plain,
! [A,C,D,F,G] :
( ( eqangle(D,A,A,F,A,C,C,G)
| eqangle(A,D,D,F,C,A,A,G)
| sP2_prd(G,F,D,C,A) )
& ( ( ~ eqangle(D,A,A,F,A,C,C,G)
& ~ eqangle(A,D,D,F,C,A,A,G) )
| ~ sP2_prd(G,F,D,C,A) ) ),
inference(NNF_transformation,[status(thm)],[f372]) ).
fof(f396,plain,
( ! [A,C,D,F,G] :
( eqangle(D,A,A,F,A,C,C,G)
| eqangle(A,D,D,F,C,A,A,G)
| sP2_prd(G,F,D,C,A) )
& ! [A,C,D,F,G] :
( ( ~ eqangle(D,A,A,F,A,C,C,G)
& ~ eqangle(A,D,D,F,C,A,A,G) )
| ~ sP2_prd(G,F,D,C,A) ) ),
inference(miniscoping,[status(thm)],[f395]) ).
fof(f397,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X4,X2,X2,X1,X3,X4,X4,X0)
| ~ sP2_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f396]) ).
fof(f398,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X2,X4,X4,X1,X4,X3,X3,X0)
| ~ sP2_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f396]) ).
fof(f399,plain,
! [X0,X1,X2,X3,X4] :
( eqangle(X2,X4,X4,X1,X4,X3,X3,X0)
| eqangle(X4,X2,X2,X1,X3,X4,X4,X0)
| sP2_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f396]) ).
fof(f400,plain,
! [A,C,D,F,G] :
( ( eqangle(D,A,A,F,A,G,G,C)
| eqangle(A,D,D,F,A,G,G,C)
| sP3_prd(G,F,D,C,A) )
& ( ( ~ eqangle(D,A,A,F,A,G,G,C)
& ~ eqangle(A,D,D,F,A,G,G,C) )
| ~ sP3_prd(G,F,D,C,A) ) ),
inference(NNF_transformation,[status(thm)],[f373]) ).
fof(f401,plain,
( ! [A,C,D,F,G] :
( eqangle(D,A,A,F,A,G,G,C)
| eqangle(A,D,D,F,A,G,G,C)
| sP3_prd(G,F,D,C,A) )
& ! [A,C,D,F,G] :
( ( ~ eqangle(D,A,A,F,A,G,G,C)
& ~ eqangle(A,D,D,F,A,G,G,C) )
| ~ sP3_prd(G,F,D,C,A) ) ),
inference(miniscoping,[status(thm)],[f400]) ).
fof(f403,plain,
! [X0,X1,X2,X3,X4] :
( ~ eqangle(X2,X4,X4,X1,X4,X0,X0,X3)
| ~ sP3_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f401]) ).
fof(f441,plain,
midp(sK26_skl,sK20_skl,sK25_skl),
inference(resolution,[status(thm)],[f122,f378]) ).
fof(f569,plain,
( ~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK20_skl,sK21_skl,sK21_skl,sK24_skl)
| ~ eqangle(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK20_skl,sK24_skl,sK24_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(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK21_skl,sK20_skl,sK20_skl,sK24_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f384,f387]) ).
fof(f1384,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( eqangle(X2,X2,X2,X1,X3,X4,X5,X6)
| ~ eqangle(X2,X2,X2,X0,X3,X4,X5,X6)
| sP2_prd(X0,X1,X2,X2,X2) ),
inference(resolution,[status(thm)],[f399,f147]) ).
fof(f1674,plain,
( ~ eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK20_skl,sK21_skl,sK21_skl,sK24_skl)
| ~ eqangle(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK20_skl,sK24_skl,sK24_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(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK21_skl,sK20_skl,sK20_skl,sK24_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f569,f403]) ).
fof(f2512,plain,
! [X0,X1] :
( para(sK20_skl,X0,sK25_skl,X1)
| ~ midp(sK26_skl,X0,X1) ),
inference(resolution,[status(thm)],[f249,f441]) ).
fof(f6215,plain,
para(sK20_skl,sK25_skl,sK25_skl,sK20_skl),
inference(resolution,[status(thm)],[f2512,f378]) ).
fof(f6230,plain,
para(sK20_skl,sK25_skl,sK20_skl,sK25_skl),
inference(resolution,[status(thm)],[f6215,f105]) ).
fof(f6250,plain,
! [X0,X1] : eqangle(sK20_skl,sK25_skl,X0,X1,sK20_skl,sK25_skl,X0,X1),
inference(resolution,[status(thm)],[f6230,f189]) ).
fof(f7022,plain,
! [X0,X1] : eqangle(sK20_skl,sK25_skl,sK20_skl,sK25_skl,X0,X1,X0,X1),
inference(resolution,[status(thm)],[f6250,f144]) ).
fof(f7024,plain,
! [X0,X1] : eqangle(X0,X1,sK20_skl,sK25_skl,X0,X1,sK20_skl,sK25_skl),
inference(resolution,[status(thm)],[f6250,f140]) ).
fof(f7993,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f7024,f186]) ).
fof(f8017,plain,
! [X0,X1] : para(X0,X1,X1,X0),
inference(resolution,[status(thm)],[f7993,f105]) ).
fof(f8018,plain,
! [X0,X1] : coll(X0,X1,X1),
inference(resolution,[status(thm)],[f7993,f256]) ).
fof(f8356,plain,
! [X0,X1] : coll(X0,X1,X0),
inference(resolution,[status(thm)],[f8018,f100]) ).
fof(f8654,plain,
! [X0,X1] : coll(X0,X0,X1),
inference(resolution,[status(thm)],[f8356,f98]) ).
fof(f8698,plain,
! [X0,X1,X2] :
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[f8654,f103]) ).
fof(f8701,plain,
! [X0,X1,X2] : coll(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f8698,f8654]) ).
fof(f8708,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,f8701]) ).
fof(f8709,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X2,X0,X3)
| ~ eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f8701]) ).
fof(f8710,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f258,f8701]) ).
fof(f8719,plain,
! [X0,X1,X2,X3] : eqangle(X0,X1,X2,X3,X1,X0,X2,X3),
inference(resolution,[status(thm)],[f8017,f189]) ).
fof(f8740,plain,
! [X0] : cyclic(sK25_skl,sK25_skl,sK20_skl,X0),
inference(resolution,[status(thm)],[f8709,f7022]) ).
fof(f8943,plain,
! [X0,X1] :
( cyclic(sK25_skl,sK20_skl,X1,X0)
| ~ cyclic(sK25_skl,sK25_skl,sK20_skl,X0) ),
inference(resolution,[status(thm)],[f8740,f136]) ).
fof(f8947,plain,
! [X0,X1] : cyclic(sK25_skl,sK20_skl,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f8943,f8740]) ).
fof(f8949,plain,
! [X0,X1,X2] :
( cyclic(sK20_skl,X0,X2,X1)
| ~ cyclic(sK25_skl,sK20_skl,X0,X1) ),
inference(resolution,[status(thm)],[f8947,f136]) ).
fof(f8953,plain,
! [X0,X1,X2] : cyclic(sK20_skl,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f8949,f8947]) ).
fof(f8955,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(sK20_skl,X0,X1,X2) ),
inference(resolution,[status(thm)],[f8953,f136]) ).
fof(f8959,plain,
! [X0,X1,X2,X3] : cyclic(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f8955,f8953]) ).
fof(f8962,plain,
! [X0,X1,X2,X3] :
( perp(X1,X0,X0,X3)
| ~ cong(X0,X3,X2,X3)
| ~ cong(X0,X1,X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f8959]) ).
fof(f8964,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,f8959]) ).
fof(f8966,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)],[f8964,f8959]) ).
fof(f9099,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)],[f8966,f8959]) ).
fof(f9101,plain,
! [X0,X1] : cong(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f9099,f8719]) ).
fof(f9227,plain,
! [X0,X1,X2] :
( perp(X2,X0,X0,X1)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f9101,f8962]) ).
fof(f9228,plain,
! [X0,X1] : midp(X0,X1,X1),
inference(resolution,[status(thm)],[f9101,f8710]) ).
fof(f9232,plain,
! [X0,X1,X2] :
( perp(X0,X0,X2,X1)
| ~ cong(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[f9101,f232]) ).
fof(f9238,plain,
! [X0,X1,X2] : perp(X0,X1,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f9227,f9101]) ).
fof(f9239,plain,
! [X0,X1,X2] : perp(X0,X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f9232,f9101]) ).
fof(f9266,plain,
! [X0,X1,X2,X3] :
( cong(X1,X0,X3,X0)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f9238]) ).
fof(f9279,plain,
! [X0,X1,X2] : perp(X0,X1,X2,X2),
inference(resolution,[status(thm)],[f9239,f114]) ).
fof(f9310,plain,
! [X0,X1,X2,X3,X4] :
( para(X3,X4,X1,X2)
| ~ perp(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f9279,f117]) ).
fof(f9314,plain,
! [X0,X1,X2,X3] : para(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f9310,f9239]) ).
fof(f9323,plain,
! [X0,X1,X2,X3,X4] :
( midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f8708,f9314]) ).
fof(f9328,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3),
inference(backward_subsumption_resolution,[status(thm)],[f189,f9314]) ).
fof(f9529,plain,
! [X0,X1,X2] : cong(X0,X1,X2,X1),
inference(resolution,[status(thm)],[f9266,f9228]) ).
fof(f9541,plain,
! [X0,X1,X2] : cong(X0,X1,X1,X2),
inference(resolution,[status(thm)],[f9529,f149]) ).
fof(f9548,plain,
! [X0,X1] : midp(X0,X0,X1),
inference(resolution,[status(thm)],[f9541,f8710]) ).
fof(f9551,plain,
! [X0,X1,X2] : cong(X0,X1,X2,X0),
inference(resolution,[status(thm)],[f9541,f151]) ).
fof(f9563,plain,
! [X0,X1] : midp(X0,X1,X0),
inference(resolution,[status(thm)],[f9548,f122]) ).
fof(f9580,plain,
! [X0,X1,X2] : cong(X0,X1,X0,X2),
inference(resolution,[status(thm)],[f9551,f149]) ).
fof(f9584,plain,
! [X0,X1,X2] : midp(X0,X1,X2),
inference(resolution,[status(thm)],[f9323,f9563]) ).
fof(f9588,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,f9584]) ).
fof(f9595,plain,
! [X0,X1,X2,X3] :
( circle(X0,X1,X2,X3)
| ~ cong(X0,X1,X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f124,f9580]) ).
fof(f9600,plain,
! [X0,X1,X2,X3] : circle(X0,X1,X2,X3),
inference(forward_subsumption_resolution,[status(thm)],[f9595,f9580]) ).
fof(f9643,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5),
inference(resolution,[status(thm)],[f9328,f144]) ).
fof(f9810,plain,
! [X0,X1,X2,X3,X4] : eqangle(X0,X1,X0,X2,X3,X1,X3,X4),
inference(forward_subsumption_resolution,[status(thm)],[f9588,f9600]) ).
fof(f9830,plain,
! [X0,X1,X2,X3,X4] : eqangle(X0,X1,X1,X2,X3,X0,X3,X4),
inference(resolution,[status(thm)],[f9810,f138]) ).
fof(f9984,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X1,X0,X1,X2,X3,X4,X5),
inference(resolution,[status(thm)],[f9643,f142]) ).
fof(f10276,plain,
! [X0,X1,X2,X3] : ~ sP2_prd(X0,X1,X2,X3,X3),
inference(resolution,[status(thm)],[f9830,f397]) ).
fof(f10282,plain,
! [X0,X1,X2,X3,X4] : eqangle(X0,X1,X0,X2,X1,X3,X3,X4),
inference(resolution,[status(thm)],[f9830,f142]) ).
fof(f10467,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( eqangle(X0,X0,X0,X6,X2,X3,X4,X5)
| ~ eqangle(X0,X0,X0,X1,X2,X3,X4,X5) ),
inference(forward_subsumption_resolution,[status(thm)],[f1384,f10276]) ).
fof(f10496,plain,
! [X0,X1,X2,X3,X4] : eqangle(X0,X0,X0,X1,X2,X3,X0,X4),
inference(resolution,[status(thm)],[f10467,f9328]) ).
fof(f10824,plain,
! [X0,X1,X2,X3,X4,X5] : eqangle(X0,X0,X0,X1,X2,X3,X4,X5),
inference(resolution,[status(thm)],[f9984,f10467]) ).
fof(f11477,plain,
! [X0,X1,X2,X3,X4] : eqangle(X0,X1,X1,X2,X0,X3,X3,X4),
inference(resolution,[status(thm)],[f10282,f138]) ).
fof(f12168,plain,
! [X0,X1,X2,X3,X4] : eqangle(X0,X1,X2,X3,X2,X2,X2,X4),
inference(resolution,[status(thm)],[f10496,f142]) ).
fof(f12831,plain,
( ~ eqangle(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK20_skl,sK24_skl,sK24_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(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK21_skl,sK20_skl,sK20_skl,sK24_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f1674,f11477]) ).
fof(f12833,plain,
! [X0,X1,X2,X3,X4] : ~ sP1_prd(X0,X1,X2,X3,X4),
inference(backward_subsumption_resolution,[status(thm)],[f392,f11477]) ).
fof(f12905,plain,
( ~ eqangle(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK20_skl,sK24_skl,sK24_skl,sK21_skl)
| sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl)
| ~ eqangle(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK21_skl,sK20_skl,sK20_skl,sK24_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f12831,f12833]) ).
fof(f13039,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( eqangle(X6,X7,X0,X8,X2,X3,X4,X5)
| ~ eqangle(X0,X0,X0,X1,X2,X3,X4,X5) ),
inference(resolution,[status(thm)],[f12168,f147]) ).
fof(f13044,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : eqangle(X0,X1,X2,X3,X4,X5,X6,X7),
inference(forward_subsumption_resolution,[status(thm)],[f13039,f10824]) ).
fof(f13773,plain,
( ~ eqangle(sK22_skl,sK20_skl,sK20_skl,sK23_skl,sK20_skl,sK24_skl,sK24_skl,sK21_skl)
| sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f12905,f13044]) ).
fof(f13775,plain,
! [X0,X1,X2,X3,X4] : ~ sP2_prd(X0,X1,X2,X3,X4),
inference(backward_subsumption_resolution,[status(thm)],[f398,f13044]) ).
fof(f13777,plain,
sP2_prd(sK24_skl,sK23_skl,sK22_skl,sK21_skl,sK20_skl),
inference(forward_subsumption_resolution,[status(thm)],[f13773,f13044]) ).
fof(f13779,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f13777,f13775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO599+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 17:51:06 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 17.14/2.62 % Refutation found
% 17.14/2.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 17.14/2.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.84/2.66 % Elapsed time: 2.275849 seconds
% 14.84/2.66 % CPU time: 17.696576 seconds
% 14.84/2.66 % Total memory used: 192.180 MB
% 14.84/2.66 % Net memory used: 175.357 MB
%------------------------------------------------------------------------------