%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO540+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:26:36 PM UTC 2026
% Result : Satisfiable 0.08s 0.41s
% Output : Saturation 0.08s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B,C,D,E,F,G,H,P,Q,U,V] :
( ( eqratio(P,Q,U,V,E,F,G,H)
& eqratio(A,B,C,D,P,Q,U,V) )
=> eqratio(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B,C,P,Q,R] :
( simtri(A,C,B,P,R,Q)
=> simtri(A,B,C,P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B,C,P,Q,R] :
( simtri(B,A,C,Q,P,R)
=> simtri(A,B,C,P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A,B,C,P,Q,R] :
( simtri(P,Q,R,A,B,C)
=> simtri(A,B,C,P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B,C,E,F,G,P,Q,R] :
( ( simtri(E,F,G,P,Q,R)
& simtri(A,B,C,E,F,G) )
=> simtri(A,B,C,P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B,C,P,Q,R] :
( contri(A,C,B,P,R,Q)
=> contri(A,B,C,P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B,C,P,Q,R] :
( contri(B,A,C,Q,P,R)
=> contri(A,B,C,P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A,B,C,P,Q,R] :
( contri(P,Q,R,A,B,C)
=> contri(A,B,C,P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B,C,E,F,G,P,Q,R] :
( ( contri(E,F,G,P,Q,R)
& contri(A,B,C,E,F,G) )
=> contri(A,B,C,P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [A,B,O] :
( ( ~ coll(O,A,B)
& eqangle(O,A,A,B,A,B,O,B) )
=> cong(O,A,O,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A,B,C,O,X] :
( ( perp(O,A,A,X)
& circle(O,A,B,C) )
=> eqangle(A,X,A,B,C,A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A,B,C,O,X] :
( ( eqangle(A,X,A,B,C,A,C,B)
& circle(O,A,B,C) )
=> perp(O,A,A,X) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [A,B,C,O,M] :
( ( eqangle(A,B,A,C,O,B,O,M)
& coll(M,B,C)
& circle(O,A,B,C) )
=> midp(M,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [A,B,C,M] :
( ( midp(M,A,C)
& perp(A,B,B,C) )
=> cong(A,M,B,M) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [A,B,C,D] :
( ( para(A,B,C,D)
& cyclic(A,B,C,D) )
=> eqangle(A,D,C,D,C,D,C,B) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [A,B,C,P,Q,R] :
( ( ~ coll(A,B,C)
& eqangle(A,C,B,C,P,R,Q,R)
& eqangle(A,B,B,C,P,Q,Q,R) )
=> simtri(A,B,C,P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [A,B,C,P,Q,R] :
( simtri(A,B,C,P,Q,R)
=> eqratio(A,B,A,C,P,Q,P,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [A,B,C,P,Q,R] :
( simtri(A,B,C,P,Q,R)
=> eqangle(A,B,B,C,P,Q,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [A,B,C,P,Q,R] :
( ( cong(A,B,P,Q)
& simtri(A,B,C,P,Q,R) )
=> contri(A,B,C,P,Q,R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [A,B,C,P,Q,R] :
( contri(A,B,C,P,Q,R)
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [A,B,C,D,M,N] :
( ( midp(N,C,D)
& midp(M,A,B) )
=> eqratio(M,A,A,B,N,C,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [A,B,C,D] :
( ( ~ para(A,B,C,D)
& eqangle(A,B,C,D,C,D,A,B) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [A,M,O,X] :
? [B] :
( ( eqangle(X,O,M,O,M,O,A,O)
& perp(O,M,M,A) )
=> ( coll(B,O,X)
& coll(B,A,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [A,B,O,X] :
? [M] :
( ( eqangle(A,O,O,X,O,X,O,B)
& cong(O,A,O,B) )
=> ( coll(M,O,X)
& coll(B,A,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [A,B,O,X] :
? [M] :
( ( eqangle(A,O,O,X,O,X,O,B)
& perp(O,X,A,B) )
=> ( coll(M,O,X)
& coll(B,A,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [A,B,O,X] :
? [M] :
( ( cong(O,A,O,B)
& perp(O,X,A,B) )
=> ( coll(M,O,X)
& coll(B,A,M) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [A,B,P,X,Y] :
? [Q] :
( ( ~ coll(A,B,P)
& eqangle(A,P,B,P,A,X,B,Y) )
=> ( cyclic(X,B,P,Q)
& eqangle(A,P,B,P,A,Q,B,Q) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [A,B,C,D,M,N] :
? [P] :
( ( midp(N,C,D)
& midp(M,A,B) )
=> ( para(P,N,A,C)
& para(P,M,B,D)
& midp(P,A,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [A,B,C,D,M,N,Q] :
? [P] :
( ( coll(D,A,B)
& coll(C,A,B)
& midp(N,C,D)
& midp(M,A,B) )
=> midp(P,A,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [A,B,M,P,Q,R,M] :
? [X] :
( ( coll(P,Q,R)
& para(A,P,B,Q)
& para(A,P,R,M)
& midp(M,A,B) )
=> ( coll(X,M,R)
& coll(X,A,Q) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [A,B,C,D,O] :
? [P] :
( ( perp(A,B,B,O)
& cong(O,C,O,D) )
=> ( cong(B,C,B,P)
& para(P,C,A,B)
& cong(O,C,O,P) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,H,A,C)
& perp(A,H,B,C) )
=> ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f88,axiom,
! [A,B,C,D,M,N] :
? [P,Q] :
( ( M != N
& cong(N,A,N,B)
& cong(M,A,M,D)
& circle(M,A,B,C) )
=> ( cong(Q,N,N,A)
& coll(Q,B,D)
& cong(P,N,N,A)
& coll(P,A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,axiom,
! [A,B,C,D,M] :
? [O] :
( ( midp(M,A,B)
& para(A,B,C,D)
& cyclic(A,B,C,D) )
=> circle(O,A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [A,B,C,D] :
? [O] :
( ( cyclic(A,B,C,D)
& perp(A,C,C,B) )
=> circle(O,A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [A,B,C,E,F] :
? [P] :
( ( coll(B,E,F)
& perp(A,C,C,B) )
=> ( perp(P,A,E,F)
& coll(P,E,F) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [A,B,C,D,M] :
? [P] :
( ( midp(M,B,D)
& perp(C,A,C,D)
& perp(A,B,A,C) )
=> midp(P,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [A,B,O] :
? [C] :
( ( perp(A,O,O,B)
& cong(O,A,O,B) )
=> ( cong(O,A,O,C)
& coll(A,O,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [A,B,C,D,P,Q] :
? [R] :
( ( coll(Q,A,B)
& coll(P,B,D)
& coll(P,A,C)
& para(A,B,C,D) )
=> ( coll(R,C,D)
& coll(P,Q,R) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f96,plain,
! [X0,X1,X2] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f98,plain,
! [X0,X1,X2] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,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(f100,plain,
! [A,C,D] :
( coll(C,D,A)
| ! [B] :
( ~ coll(A,B,D)
| ~ coll(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f107,plain,
! [A,B,E,F] :
( para(A,B,E,F)
| ! [C,D] :
( ~ para(C,D,E,F)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,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(f114,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)],[f113]) ).
fof(f115,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)],[f114]) ).
fof(f116,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(f117,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)],[f116]) ).
fof(f118,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)],[f117]) ).
fof(f119,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f120,plain,
! [X0,X1,X2] :
( midp(X0,X2,X1)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,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(f122,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)],[f121]) ).
fof(f123,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(f124,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)],[f123]) ).
fof(f125,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)],[f124]) ).
fof(f126,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f132,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(f133,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)],[f132]) ).
fof(f134,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)],[f133]) ).
fof(f135,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(f136,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)],[f135]) ).
fof(f137,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(f138,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)],[f137]) ).
fof(f139,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(f140,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)],[f139]) ).
fof(f141,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(f142,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)],[f141]) ).
fof(f143,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(f144,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)],[f143]) ).
fof(f145,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)],[f144]) ).
fof(f146,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f147,plain,
! [X0,X1,X2,X3] :
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,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(f151,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)],[f150]) ).
fof(f152,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)],[f151]) ).
fof(f153,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(B,A,C,D,P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqratio(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(C,D,A,B,U,V,P,Q)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqratio(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f157,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(P,Q,U,V,A,B,C,D)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f158,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqratio(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f159,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqratio(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
! [A,B,C,D,E,F,G,H,P,Q,U,V] :
( eqratio(A,B,C,D,E,F,G,H)
| ~ eqratio(P,Q,U,V,E,F,G,H)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f162,plain,
! [A,B,C,D,E,F,G,H] :
( eqratio(A,B,C,D,E,F,G,H)
| ! [P,Q,U,V] :
( ~ eqratio(P,Q,U,V,E,F,G,H)
| ~ eqratio(A,B,C,D,P,Q,U,V) ) ),
inference(miniscoping,[status(thm)],[f161]) ).
fof(f163,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( eqratio(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqratio(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f164,plain,
! [A,B,C,P,Q,R] :
( simtri(A,B,C,P,Q,R)
| ~ simtri(A,C,B,P,R,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4,X5] :
( simtri(X0,X2,X1,X3,X5,X4)
| ~ simtri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f166,plain,
! [A,B,C,P,Q,R] :
( simtri(A,B,C,P,Q,R)
| ~ simtri(B,A,C,Q,P,R) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f167,plain,
! [X0,X1,X2,X3,X4,X5] :
( simtri(X1,X0,X2,X4,X3,X5)
| ~ simtri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f168,plain,
! [A,B,C,P,Q,R] :
( simtri(A,B,C,P,Q,R)
| ~ simtri(P,Q,R,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f169,plain,
! [X0,X1,X2,X3,X4,X5] :
( simtri(X3,X4,X5,X0,X1,X2)
| ~ simtri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f170,plain,
! [A,B,C,E,F,G,P,Q,R] :
( simtri(A,B,C,P,Q,R)
| ~ simtri(E,F,G,P,Q,R)
| ~ simtri(A,B,C,E,F,G) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f171,plain,
! [A,B,C,P,Q,R] :
( simtri(A,B,C,P,Q,R)
| ! [E,F,G] :
( ~ simtri(E,F,G,P,Q,R)
| ~ simtri(A,B,C,E,F,G) ) ),
inference(miniscoping,[status(thm)],[f170]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( simtri(X0,X1,X2,X6,X7,X8)
| ~ simtri(X3,X4,X5,X6,X7,X8)
| ~ simtri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
! [A,B,C,P,Q,R] :
( contri(A,B,C,P,Q,R)
| ~ contri(A,C,B,P,R,Q) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f174,plain,
! [X0,X1,X2,X3,X4,X5] :
( contri(X0,X2,X1,X3,X5,X4)
| ~ contri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f175,plain,
! [A,B,C,P,Q,R] :
( contri(A,B,C,P,Q,R)
| ~ contri(B,A,C,Q,P,R) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f176,plain,
! [X0,X1,X2,X3,X4,X5] :
( contri(X1,X0,X2,X4,X3,X5)
| ~ contri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f177,plain,
! [A,B,C,P,Q,R] :
( contri(A,B,C,P,Q,R)
| ~ contri(P,Q,R,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f178,plain,
! [X0,X1,X2,X3,X4,X5] :
( contri(X3,X4,X5,X0,X1,X2)
| ~ contri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f177]) ).
fof(f179,plain,
! [A,B,C,E,F,G,P,Q,R] :
( contri(A,B,C,P,Q,R)
| ~ contri(E,F,G,P,Q,R)
| ~ contri(A,B,C,E,F,G) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f180,plain,
! [A,B,C,P,Q,R] :
( contri(A,B,C,P,Q,R)
| ! [E,F,G] :
( ~ contri(E,F,G,P,Q,R)
| ~ contri(A,B,C,E,F,G) ) ),
inference(miniscoping,[status(thm)],[f179]) ).
fof(f181,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( contri(X0,X1,X2,X6,X7,X8)
| ~ contri(X3,X4,X5,X6,X7,X8)
| ~ contri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f182,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(f183,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)],[f182]) ).
fof(f184,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)],[f183]) ).
fof(f185,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(f186,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)],[f185]) ).
fof(f187,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)],[f186]) ).
fof(f188,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(f189,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f190,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(f191,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)],[f190]) ).
fof(f192,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(f193,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)],[f192]) ).
fof(f194,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(f195,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)],[f194]) ).
fof(f196,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)],[f195]) ).
fof(f197,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(f198,plain,
! [B,C,E,F] :
( para(E,F,B,C)
| ! [A] :
( ~ midp(F,A,C)
| ~ midp(E,A,B) ) ),
inference(miniscoping,[status(thm)],[f197]) ).
fof(f199,plain,
! [X0,X1,X2,X3,X4] :
( para(X0,X3,X2,X4)
| ~ midp(X3,X1,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f200,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(f201,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)],[f200]) ).
fof(f202,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)],[f201]) ).
fof(f203,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(f204,plain,
! [X0,X1,X2] :
( eqangle(X0,X1,X1,X2,X1,X2,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f205,plain,
! [A,B,O] :
( cong(O,A,O,B)
| coll(O,A,B)
| ~ eqangle(O,A,A,B,A,B,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f206,plain,
! [X0,X1,X2] :
( cong(X0,X1,X0,X2)
| coll(X0,X1,X2)
| ~ eqangle(X0,X1,X1,X2,X1,X2,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f207,plain,
! [A,B,C,O,X] :
( eqangle(A,X,A,B,C,A,C,B)
| ~ perp(O,A,A,X)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f208,plain,
! [A,B,C,X] :
( eqangle(A,X,A,B,C,A,C,B)
| ! [O] :
( ~ perp(O,A,A,X)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f207]) ).
fof(f209,plain,
! [X0,X1,X2,X3,X4] :
( eqangle(X1,X4,X1,X2,X3,X1,X3,X2)
| ~ perp(X0,X1,X1,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
! [A,B,C,O,X] :
( perp(O,A,A,X)
| ~ eqangle(A,X,A,B,C,A,C,B)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f211,plain,
! [A,O,X] :
( perp(O,A,A,X)
| ! [B,C] :
( ~ eqangle(A,X,A,B,C,A,C,B)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f210]) ).
fof(f212,plain,
! [X0,X1,X2,X3,X4] :
( perp(X0,X1,X1,X4)
| ~ eqangle(X1,X4,X1,X2,X3,X1,X3,X2)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f213,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(f214,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)],[f213]) ).
fof(f215,plain,
! [A,B,C,O,M] :
( midp(M,B,C)
| ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f216,plain,
! [B,C,M] :
( midp(M,B,C)
| ! [A,O] :
( ~ eqangle(A,B,A,C,O,B,O,M)
| ~ coll(M,B,C)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f215]) ).
fof(f217,plain,
! [X0,X1,X2,X3,X4] :
( midp(X4,X2,X3)
| ~ eqangle(X1,X2,X1,X3,X0,X2,X0,X4)
| ~ coll(X4,X2,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f218,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(f219,plain,
! [A,B,M] :
( cong(A,M,B,M)
| ! [C] :
( ~ midp(M,A,C)
| ~ perp(A,B,B,C) ) ),
inference(miniscoping,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0,X1,X2,X3] :
( cong(X0,X3,X1,X3)
| ~ midp(X3,X0,X2)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f221,plain,
! [A,B,C,O] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f222,plain,
! [A,B,C] :
( perp(A,B,B,C)
| ! [O] :
( ~ coll(O,A,C)
| ~ circle(O,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f221]) ).
fof(f223,plain,
! [X0,X1,X2,X3] :
( perp(X1,X2,X2,X3)
| ~ coll(X0,X1,X3)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f222]) ).
fof(f224,plain,
! [A,B,C,D] :
( eqangle(A,D,C,D,C,D,C,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f225,plain,
! [X0,X1,X2,X3] :
( eqangle(X0,X3,X2,X3,X2,X3,X2,X1)
| ~ para(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f226,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(f227,plain,
! [A,B,O] :
( cong(O,A,O,B)
| ! [M] :
( ~ perp(O,M,A,B)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( cong(X3,X1,X3,X2)
| ~ perp(X3,X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f229,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(f230,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)],[f229]) ).
fof(f231,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(f232,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)],[f231]) ).
fof(f233,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)],[f232]) ).
fof(f234,plain,
! [A,B,C,P,Q,R] :
( simtri(A,B,C,P,Q,R)
| coll(A,B,C)
| ~ eqangle(A,C,B,C,P,R,Q,R)
| ~ eqangle(A,B,B,C,P,Q,Q,R) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f235,plain,
! [X0,X1,X2,X3,X4,X5] :
( simtri(X0,X1,X2,X3,X4,X5)
| coll(X0,X1,X2)
| ~ eqangle(X0,X2,X1,X2,X3,X5,X4,X5)
| ~ eqangle(X0,X1,X1,X2,X3,X4,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f236,plain,
! [A,B,C,P,Q,R] :
( eqratio(A,B,A,C,P,Q,P,R)
| ~ simtri(A,B,C,P,Q,R) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f237,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqratio(X0,X1,X0,X2,X3,X4,X3,X5)
| ~ simtri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f236]) ).
fof(f238,plain,
! [A,B,C,P,Q,R] :
( eqangle(A,B,B,C,P,Q,Q,R)
| ~ simtri(A,B,C,P,Q,R) ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f239,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X1,X2,X3,X4,X4,X5)
| ~ simtri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f240,plain,
! [A,B,C,P,Q,R] :
( contri(A,B,C,P,Q,R)
| ~ cong(A,B,P,Q)
| ~ simtri(A,B,C,P,Q,R) ),
inference(pre_NNF_transformation,[status(thm)],[f62]) ).
fof(f241,plain,
! [X0,X1,X2,X3,X4,X5] :
( contri(X0,X1,X2,X3,X4,X5)
| ~ cong(X0,X1,X3,X4)
| ~ simtri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f242,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ contri(A,B,C,P,Q,R) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f243,plain,
! [A,B,P,Q] :
( cong(A,B,P,Q)
| ! [C,R] : ~ contri(A,B,C,P,Q,R) ),
inference(miniscoping,[status(thm)],[f242]) ).
fof(f244,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ contri(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f243]) ).
fof(f245,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(f246,plain,
! [A,B,C,D] :
( para(A,C,B,D)
| ! [M] :
( ~ midp(M,C,D)
| ~ midp(M,A,B) ) ),
inference(miniscoping,[status(thm)],[f245]) ).
fof(f247,plain,
! [X0,X1,X2,X3,X4] :
( para(X1,X3,X2,X4)
| ~ midp(X0,X3,X4)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f248,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(f249,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)],[f248]) ).
fof(f250,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)],[f249]) ).
fof(f251,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f66]) ).
fof(f252,plain,
! [X0,X1,X2,X3,X4] :
( eqratio(X4,X0,X0,X2,X4,X1,X1,X3)
| ~ coll(X4,X1,X3)
| ~ coll(X4,X0,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f251]) ).
fof(f253,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f254,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f255,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(f256,plain,
! [X0,X1,X2] :
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f258,plain,
! [X0,X1,X2] :
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f259,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f70]) ).
fof(f260,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f261,plain,
! [A,B,C,D,M,N] :
( eqratio(M,A,A,B,N,C,C,D)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f71]) ).
fof(f262,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqratio(X0,X1,X1,X2,X3,X4,X4,X5)
| ~ midp(X3,X4,X5)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f263,plain,
! [A,B,C,D] :
( perp(A,B,C,D)
| para(A,B,C,D)
| ~ eqangle(A,B,C,D,C,D,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f72]) ).
fof(f264,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
| para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X2,X3,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f263]) ).
fof(f267,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f74]) ).
fof(f268,plain,
! [A,B,C,D] :
( para(A,B,C,D)
| ! [P,Q,U,V] :
( ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ) ),
inference(miniscoping,[status(thm)],[f267]) ).
fof(f269,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f268]) ).
fof(f270,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f271,plain,
! [A,B,C,D] :
( perp(A,B,C,D)
| ! [P,Q,U,V] :
( ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ) ),
inference(miniscoping,[status(thm)],[f270]) ).
fof(f272,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f273,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(pre_NNF_transformation,[status(thm)],[f76]) ).
fof(f274,plain,
! [A,B,C,D] :
( cong(A,B,C,D)
| ! [P,Q,U,V] :
( ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ) ),
inference(miniscoping,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( cong(X0,X1,X2,X3)
| ~ cong(X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f276,plain,
! [A,M,O,X] :
? [B] :
( ( coll(B,O,X)
& coll(B,A,M) )
| ~ eqangle(X,O,M,O,M,O,A,O)
| ~ perp(O,M,M,A) ),
inference(pre_NNF_transformation,[status(thm)],[f77]) ).
fof(f277,plain,
! [A,M,O,X] :
( ? [B] :
( coll(B,O,X)
& coll(B,A,M) )
| ~ eqangle(X,O,M,O,M,O,A,O)
| ~ perp(O,M,M,A) ),
inference(miniscoping,[status(thm)],[f276]) ).
fof(f278,plain,
! [A,M,O,X] :
( ( coll(sK0_skl(X,O,M,A),O,X)
& coll(sK0_skl(X,O,M,A),A,M) )
| ~ eqangle(X,O,M,O,M,O,A,O)
| ~ perp(O,M,M,A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(X,O,M,A))],[f277]) ).
fof(f279,plain,
! [X0,X1,X2,X3] :
( coll(sK0_skl(X3,X0,X1,X2),X2,X1)
| ~ eqangle(X3,X0,X1,X0,X1,X0,X2,X0)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f280,plain,
! [X0,X1,X2,X3] :
( coll(sK0_skl(X3,X0,X1,X2),X0,X3)
| ~ eqangle(X3,X0,X1,X0,X1,X0,X2,X0)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f281,plain,
! [A,B,O,X] :
? [M] :
( ( coll(M,O,X)
& coll(B,A,M) )
| ~ eqangle(A,O,O,X,O,X,O,B)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f78]) ).
fof(f282,plain,
! [A,B,O,X] :
( ? [M] :
( coll(M,O,X)
& coll(B,A,M) )
| ~ eqangle(A,O,O,X,O,X,O,B)
| ~ cong(O,A,O,B) ),
inference(miniscoping,[status(thm)],[f281]) ).
fof(f283,plain,
! [A,B,O,X] :
( ( coll(sK1_skl(X,O,B,A),O,X)
& coll(B,A,sK1_skl(X,O,B,A)) )
| ~ eqangle(A,O,O,X,O,X,O,B)
| ~ cong(O,A,O,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(M,sK1_skl(X,O,B,A))],[f282]) ).
fof(f284,plain,
! [X0,X1,X2,X3] :
( coll(X2,X1,sK1_skl(X3,X0,X2,X1))
| ~ eqangle(X1,X0,X0,X3,X0,X3,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f285,plain,
! [X0,X1,X2,X3] :
( coll(sK1_skl(X3,X0,X2,X1),X0,X3)
| ~ eqangle(X1,X0,X0,X3,X0,X3,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f286,plain,
! [A,B,O,X] :
? [M] :
( ( coll(M,O,X)
& coll(B,A,M) )
| ~ eqangle(A,O,O,X,O,X,O,B)
| ~ perp(O,X,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f287,plain,
! [A,B,O,X] :
( ? [M] :
( coll(M,O,X)
& coll(B,A,M) )
| ~ eqangle(A,O,O,X,O,X,O,B)
| ~ perp(O,X,A,B) ),
inference(miniscoping,[status(thm)],[f286]) ).
fof(f288,plain,
! [A,B,O,X] :
( ( coll(sK2_skl(X,O,B,A),O,X)
& coll(B,A,sK2_skl(X,O,B,A)) )
| ~ eqangle(A,O,O,X,O,X,O,B)
| ~ perp(O,X,A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(M,sK2_skl(X,O,B,A))],[f287]) ).
fof(f289,plain,
! [X0,X1,X2,X3] :
( coll(X3,X2,sK2_skl(X1,X0,X3,X2))
| ~ eqangle(X2,X0,X0,X1,X0,X1,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f288]) ).
fof(f290,plain,
! [X0,X1,X2,X3] :
( coll(sK2_skl(X1,X0,X3,X2),X0,X1)
| ~ eqangle(X2,X0,X0,X1,X0,X1,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f288]) ).
fof(f291,plain,
! [A,B,O,X] :
? [M] :
( ( coll(M,O,X)
& coll(B,A,M) )
| ~ cong(O,A,O,B)
| ~ perp(O,X,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f292,plain,
! [A,B,O,X] :
( ? [M] :
( coll(M,O,X)
& coll(B,A,M) )
| ~ cong(O,A,O,B)
| ~ perp(O,X,A,B) ),
inference(miniscoping,[status(thm)],[f291]) ).
fof(f293,plain,
! [A,B,O,X] :
( ( coll(sK3_skl(X,O,B,A),O,X)
& coll(B,A,sK3_skl(X,O,B,A)) )
| ~ cong(O,A,O,B)
| ~ perp(O,X,A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(M,sK3_skl(X,O,B,A))],[f292]) ).
fof(f294,plain,
! [X0,X1,X2,X3] :
( coll(X3,X2,sK3_skl(X1,X0,X3,X2))
| ~ cong(X0,X2,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f293]) ).
fof(f295,plain,
! [X0,X1,X2,X3] :
( coll(sK3_skl(X1,X0,X3,X2),X0,X1)
| ~ cong(X0,X2,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f293]) ).
fof(f296,plain,
! [A,B,P,X,Y] :
? [Q] :
( ( cyclic(X,B,P,Q)
& eqangle(A,P,B,P,A,Q,B,Q) )
| coll(A,B,P)
| ~ eqangle(A,P,B,P,A,X,B,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f297,plain,
! [A,B,P,X] :
( ? [Q] :
( cyclic(X,B,P,Q)
& eqangle(A,P,B,P,A,Q,B,Q) )
| coll(A,B,P)
| ! [Y] : ~ eqangle(A,P,B,P,A,X,B,Y) ),
inference(miniscoping,[status(thm)],[f296]) ).
fof(f298,plain,
! [A,B,P,X] :
( ( cyclic(X,B,P,sK4_skl(X,P,B,A))
& eqangle(A,P,B,P,A,sK4_skl(X,P,B,A),B,sK4_skl(X,P,B,A)) )
| coll(A,B,P)
| ! [Y] : ~ eqangle(A,P,B,P,A,X,B,Y) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Q,sK4_skl(X,P,B,A))],[f297]) ).
fof(f299,plain,
! [X0,X1,X2,X3,X4] :
( eqangle(X0,X1,X2,X1,X0,sK4_skl(X3,X1,X2,X0),X2,sK4_skl(X3,X1,X2,X0))
| coll(X0,X2,X1)
| ~ eqangle(X0,X1,X2,X1,X0,X3,X2,X4) ),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f300,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X3,X2,X1,sK4_skl(X3,X1,X2,X0))
| coll(X0,X2,X1)
| ~ eqangle(X0,X1,X2,X1,X0,X3,X2,X4) ),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f301,plain,
! [A,B,C,D,M,N] :
? [P] :
( ( para(P,N,A,C)
& para(P,M,B,D)
& midp(P,A,D) )
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f302,plain,
! [A,B,C,D,M,N] :
( ? [P] :
( para(P,N,A,C)
& para(P,M,B,D)
& midp(P,A,D) )
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(miniscoping,[status(thm)],[f301]) ).
fof(f303,plain,
! [A,B,C,D,M,N] :
( ( para(sK5_skl(N,M,D,C,B,A),N,A,C)
& para(sK5_skl(N,M,D,C,B,A),M,B,D)
& midp(sK5_skl(N,M,D,C,B,A),A,D) )
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(P,sK5_skl(N,M,D,C,B,A))],[f302]) ).
fof(f304,plain,
! [X0,X1,X2,X3,X4,X5] :
( midp(sK5_skl(X3,X0,X5,X4,X2,X1),X1,X5)
| ~ midp(X3,X4,X5)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f303]) ).
fof(f305,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(sK5_skl(X3,X0,X5,X4,X2,X1),X0,X2,X5)
| ~ midp(X3,X4,X5)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f303]) ).
fof(f306,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(sK5_skl(X3,X0,X5,X4,X2,X1),X3,X1,X4)
| ~ midp(X3,X4,X5)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f303]) ).
fof(f307,plain,
! [A,B,C,D,M,N,Q] :
? [P] :
( midp(P,A,Q)
| ~ coll(D,A,B)
| ~ coll(C,A,B)
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f308,plain,
! [A] :
( ! [Q] :
? [P] : midp(P,A,Q)
| ! [B,D] :
( ~ coll(D,A,B)
| ! [C] :
( ~ coll(C,A,B)
| ! [N] : ~ midp(N,C,D)
| ! [M] : ~ midp(M,A,B) ) ) ),
inference(miniscoping,[status(thm)],[f307]) ).
fof(f309,plain,
! [A] :
( ! [Q] : midp(sK6_skl(Q,A),A,Q)
| ! [B,D] :
( ~ coll(D,A,B)
| ! [C] :
( ~ coll(C,A,B)
| ! [N] : ~ midp(N,C,D)
| ! [M] : ~ midp(M,A,B) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(P,sK6_skl(Q,A))],[f308]) ).
fof(f310,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( midp(sK6_skl(X6,X1),X1,X6)
| ~ coll(X5,X1,X2)
| ~ coll(X4,X1,X2)
| ~ midp(X3,X4,X5)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f309]) ).
fof(f311,plain,
! [A,B,M,P,Q,R,M] :
? [X] :
( ( coll(X,M,R)
& coll(X,A,Q) )
| ~ coll(P,Q,R)
| ~ para(A,P,B,Q)
| ~ para(A,P,R,M)
| ~ midp(M,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f312,plain,
! [A,Q,R,M] :
( ? [X] :
( coll(X,M,R)
& coll(X,A,Q) )
| ! [P] :
( ~ coll(P,Q,R)
| ! [B] :
( ~ para(A,P,B,Q)
| ~ para(A,P,R,M)
| ~ midp(M,A,B) ) ) ),
inference(miniscoping,[status(thm)],[f311]) ).
fof(f313,plain,
! [A,Q,R,M] :
( ( coll(sK7_skl(M,R,Q,A),M,R)
& coll(sK7_skl(M,R,Q,A),A,Q) )
| ! [P] :
( ~ coll(P,Q,R)
| ! [B] :
( ~ para(A,P,B,Q)
| ~ para(A,P,R,M)
| ~ midp(M,A,B) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(X,sK7_skl(M,R,Q,A))],[f312]) ).
fof(f314,plain,
! [X0,X1,X2,X3,X4,X5] :
( coll(sK7_skl(X0,X4,X5,X1),X1,X5)
| ~ coll(X3,X5,X4)
| ~ para(X1,X3,X2,X5)
| ~ para(X1,X3,X4,X0)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f313]) ).
fof(f315,plain,
! [X0,X1,X2,X3,X4,X5] :
( coll(sK7_skl(X0,X4,X5,X1),X0,X4)
| ~ coll(X3,X5,X4)
| ~ para(X1,X3,X2,X5)
| ~ para(X1,X3,X4,X0)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f313]) ).
fof(f316,plain,
! [A,B,C,D,O] :
? [P] :
( ( cong(B,C,B,P)
& para(P,C,A,B)
& cong(O,C,O,P) )
| ~ perp(A,B,B,O)
| ~ cong(O,C,O,D) ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f317,plain,
! [A,B,C,O] :
( ? [P] :
( cong(B,C,B,P)
& para(P,C,A,B)
& cong(O,C,O,P) )
| ~ perp(A,B,B,O)
| ! [D] : ~ cong(O,C,O,D) ),
inference(miniscoping,[status(thm)],[f316]) ).
fof(f318,plain,
! [A,B,C,O] :
( ( cong(B,C,B,sK8_skl(O,C,B,A))
& para(sK8_skl(O,C,B,A),C,A,B)
& cong(O,C,O,sK8_skl(O,C,B,A)) )
| ~ perp(A,B,B,O)
| ! [D] : ~ cong(O,C,O,D) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(P,sK8_skl(O,C,B,A))],[f317]) ).
fof(f319,plain,
! [X0,X1,X2,X3,X4] :
( cong(X0,X1,X0,sK8_skl(X0,X1,X4,X3))
| ~ perp(X3,X4,X4,X0)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f320,plain,
! [X0,X1,X2,X3,X4] :
( para(sK8_skl(X0,X1,X4,X3),X1,X3,X4)
| ~ perp(X3,X4,X4,X0)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f321,plain,
! [X0,X1,X2,X3,X4] :
( cong(X4,X1,X4,sK8_skl(X0,X1,X4,X3))
| ~ perp(X3,X4,X4,X0)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f322,plain,
! [A,B,C,H] :
? [P,Q] :
( ( perp(B,Q,C,A)
& coll(Q,C,A)
& perp(A,P,C,B)
& coll(P,C,B) )
| ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f86]) ).
fof(f323,plain,
! [A,B,C] :
( ? [Q] :
( perp(B,Q,C,A)
& coll(Q,C,A)
& ? [P] :
( perp(A,P,C,B)
& coll(P,C,B) ) )
| ! [H] :
( ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ) ),
inference(miniscoping,[status(thm)],[f322]) ).
fof(f324,plain,
! [A,B,C] :
( ( perp(B,sK9_skl(C,B,A),C,A)
& coll(sK9_skl(C,B,A),C,A)
& perp(A,sK10_skl(C,B,A),C,B)
& coll(sK10_skl(C,B,A),C,B) )
| ! [H] :
( ~ perp(B,H,A,C)
| ~ perp(A,H,B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(Q,sK9_skl(C,B,A)),skolemize(P,sK10_skl(C,B,A))],[f323]) ).
fof(f325,plain,
! [X0,X1,X2,X3] :
( coll(sK10_skl(X3,X2,X0),X3,X2)
| ~ perp(X2,X1,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
! [X0,X1,X2,X3] :
( perp(X0,sK10_skl(X3,X2,X0),X3,X2)
| ~ perp(X2,X1,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f327,plain,
! [X0,X1,X2,X3] :
( coll(sK9_skl(X3,X2,X0),X3,X0)
| ~ perp(X2,X1,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f328,plain,
! [X0,X1,X2,X3] :
( perp(X2,sK9_skl(X3,X2,X0),X3,X0)
| ~ perp(X2,X1,X0,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f329,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f330,plain,
! [A,O] :
( ? [P] : perp(P,A,A,O)
| ! [B,C] : ~ circle(O,A,B,C) ),
inference(miniscoping,[status(thm)],[f329]) ).
fof(f331,plain,
! [A,O] :
( perp(sK11_skl(O,A),A,A,O)
| ! [B,C] : ~ circle(O,A,B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(P,sK11_skl(O,A))],[f330]) ).
fof(f332,plain,
! [X0,X1,X2,X3] :
( perp(sK11_skl(X0,X1),X1,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f333,plain,
! [A,B,C,D,M,N] :
? [P,Q] :
( ( cong(Q,N,N,A)
& coll(Q,B,D)
& cong(P,N,N,A)
& coll(P,A,C) )
| M = N
| ~ cong(N,A,N,B)
| ~ cong(M,A,M,D)
| ~ circle(M,A,B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f88]) ).
fof(f334,plain,
! [A,B,C,D,N] :
( ? [Q] :
( cong(Q,N,N,A)
& coll(Q,B,D)
& ? [P] :
( cong(P,N,N,A)
& coll(P,A,C) ) )
| ! [M] :
( M = N
| ~ cong(N,A,N,B)
| ~ cong(M,A,M,D)
| ~ circle(M,A,B,C) ) ),
inference(miniscoping,[status(thm)],[f333]) ).
fof(f335,plain,
! [A,B,C,D,N] :
( ( cong(sK12_skl(N,D,C,B,A),N,N,A)
& coll(sK12_skl(N,D,C,B,A),B,D)
& cong(sK13_skl(N,D,C,B,A),N,N,A)
& coll(sK13_skl(N,D,C,B,A),A,C) )
| ! [M] :
( M = N
| ~ cong(N,A,N,B)
| ~ cong(M,A,M,D)
| ~ circle(M,A,B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(Q,sK12_skl(N,D,C,B,A)),skolemize(P,sK13_skl(N,D,C,B,A))],[f334]) ).
fof(f336,plain,
! [X0,X1,X2,X3,X4,X5] :
( coll(sK13_skl(X5,X4,X3,X2,X1),X1,X3)
| X0 = X5
| ~ cong(X5,X1,X5,X2)
| ~ cong(X0,X1,X0,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f337,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(sK13_skl(X5,X4,X3,X2,X1),X5,X5,X1)
| X0 = X5
| ~ cong(X5,X1,X5,X2)
| ~ cong(X0,X1,X0,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f338,plain,
! [X0,X1,X2,X3,X4,X5] :
( coll(sK12_skl(X5,X4,X3,X2,X1),X2,X4)
| X0 = X5
| ~ cong(X5,X1,X5,X2)
| ~ cong(X0,X1,X0,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f339,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(sK12_skl(X5,X4,X3,X2,X1),X5,X5,X1)
| X0 = X5
| ~ cong(X5,X1,X5,X2)
| ~ cong(X0,X1,X0,X4)
| ~ circle(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f340,plain,
! [A,B,C,D,M] :
? [O] :
( circle(O,A,B,C)
| ~ midp(M,A,B)
| ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f89]) ).
fof(f341,plain,
! [A,B,C] :
( ? [O] : circle(O,A,B,C)
| ! [M] : ~ midp(M,A,B)
| ! [D] :
( ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f340]) ).
fof(f342,plain,
! [A,B,C] :
( circle(sK14_skl(C,B,A),A,B,C)
| ! [M] : ~ midp(M,A,B)
| ! [D] :
( ~ para(A,B,C,D)
| ~ cyclic(A,B,C,D) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(O,sK14_skl(C,B,A))],[f341]) ).
fof(f343,plain,
! [X0,X1,X2,X3,X4] :
( circle(sK14_skl(X2,X1,X0),X0,X1,X2)
| ~ midp(X4,X0,X1)
| ~ para(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f342]) ).
fof(f344,plain,
! [A,B,C,D] :
? [O] :
( circle(O,A,B,C)
| ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f345,plain,
! [A,B,C] :
( ? [O] : circle(O,A,B,C)
| ! [D] : ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(miniscoping,[status(thm)],[f344]) ).
fof(f346,plain,
! [A,B,C] :
( circle(sK15_skl(C,B,A),A,B,C)
| ! [D] : ~ cyclic(A,B,C,D)
| ~ perp(A,C,C,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(O,sK15_skl(C,B,A))],[f345]) ).
fof(f347,plain,
! [X0,X1,X2,X3] :
( circle(sK15_skl(X1,X2,X0),X0,X2,X1)
| ~ cyclic(X0,X2,X1,X3)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f346]) ).
fof(f348,plain,
! [A,B,C,E,F] :
? [P] :
( ( perp(P,A,E,F)
& coll(P,E,F) )
| ~ coll(B,E,F)
| ~ perp(A,C,C,B) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f349,plain,
! [A,E,F] :
( ? [P] :
( perp(P,A,E,F)
& coll(P,E,F) )
| ! [B] :
( ~ coll(B,E,F)
| ! [C] : ~ perp(A,C,C,B) ) ),
inference(miniscoping,[status(thm)],[f348]) ).
fof(f350,plain,
! [A,E,F] :
( ( perp(sK16_skl(F,E,A),A,E,F)
& coll(sK16_skl(F,E,A),E,F) )
| ! [B] :
( ~ coll(B,E,F)
| ! [C] : ~ perp(A,C,C,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(P,sK16_skl(F,E,A))],[f349]) ).
fof(f351,plain,
! [X0,X1,X2,X3,X4] :
( coll(sK16_skl(X4,X3,X0),X3,X4)
| ~ coll(X2,X3,X4)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f350]) ).
fof(f352,plain,
! [X0,X1,X2,X3,X4] :
( perp(sK16_skl(X4,X3,X0),X0,X3,X4)
| ~ coll(X2,X3,X4)
| ~ perp(X0,X1,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f350]) ).
fof(f353,plain,
! [A,B,C,D,M] :
? [P] :
( midp(P,A,C)
| ~ midp(M,B,D)
| ~ perp(C,A,C,D)
| ~ perp(A,B,A,C) ),
inference(pre_NNF_transformation,[status(thm)],[f92]) ).
fof(f354,plain,
! [A,C] :
( ? [P] : midp(P,A,C)
| ! [B,D] :
( ! [M] : ~ midp(M,B,D)
| ~ perp(C,A,C,D)
| ~ perp(A,B,A,C) ) ),
inference(miniscoping,[status(thm)],[f353]) ).
fof(f355,plain,
! [A,C] :
( midp(sK17_skl(C,A),A,C)
| ! [B,D] :
( ! [M] : ~ midp(M,B,D)
| ~ perp(C,A,C,D)
| ~ perp(A,B,A,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(P,sK17_skl(C,A))],[f354]) ).
fof(f356,plain,
! [X0,X1,X2,X3,X4] :
( midp(sK17_skl(X2,X0),X0,X2)
| ~ midp(X4,X1,X3)
| ~ perp(X2,X0,X2,X3)
| ~ perp(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f355]) ).
fof(f357,plain,
! [A,B,O] :
? [C] :
( ( cong(O,A,O,C)
& coll(A,O,C) )
| ~ perp(A,O,O,B)
| ~ cong(O,A,O,B) ),
inference(pre_NNF_transformation,[status(thm)],[f93]) ).
fof(f358,plain,
! [A,O] :
( ? [C] :
( cong(O,A,O,C)
& coll(A,O,C) )
| ! [B] :
( ~ perp(A,O,O,B)
| ~ cong(O,A,O,B) ) ),
inference(miniscoping,[status(thm)],[f357]) ).
fof(f359,plain,
! [A,O] :
( ( cong(O,A,O,sK18_skl(O,A))
& coll(A,O,sK18_skl(O,A)) )
| ! [B] :
( ~ perp(A,O,O,B)
| ~ cong(O,A,O,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(C,sK18_skl(O,A))],[f358]) ).
fof(f360,plain,
! [X0,X1,X2] :
( coll(X1,X0,sK18_skl(X0,X1))
| ~ perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f359]) ).
fof(f361,plain,
! [X0,X1,X2] :
( cong(X0,X1,X0,sK18_skl(X0,X1))
| ~ perp(X1,X0,X0,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f359]) ).
fof(f362,plain,
! [A,B,C,D,P,Q] :
? [R] :
( ( coll(R,C,D)
& coll(P,Q,R) )
| ~ coll(Q,A,B)
| ~ coll(P,B,D)
| ~ coll(P,A,C)
| ~ para(A,B,C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f94]) ).
fof(f363,plain,
! [C,D,P,Q] :
( ? [R] :
( coll(R,C,D)
& coll(P,Q,R) )
| ! [A,B] :
( ~ coll(Q,A,B)
| ~ coll(P,B,D)
| ~ coll(P,A,C)
| ~ para(A,B,C,D) ) ),
inference(miniscoping,[status(thm)],[f362]) ).
fof(f364,plain,
! [C,D,P,Q] :
( ( coll(sK19_skl(Q,P,D,C),C,D)
& coll(P,Q,sK19_skl(Q,P,D,C)) )
| ! [A,B] :
( ~ coll(Q,A,B)
| ~ coll(P,B,D)
| ~ coll(P,A,C)
| ~ para(A,B,C,D) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(R,sK19_skl(Q,P,D,C))],[f363]) ).
fof(f365,plain,
! [X0,X1,X2,X3,X4,X5] :
( coll(X4,X5,sK19_skl(X5,X4,X3,X2))
| ~ coll(X5,X0,X1)
| ~ coll(X4,X1,X3)
| ~ coll(X4,X0,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f364]) ).
fof(f366,plain,
! [X0,X1,X2,X3,X4,X5] :
( coll(sK19_skl(X5,X4,X3,X2),X2,X3)
| ~ coll(X5,X0,X1)
| ~ coll(X4,X1,X3)
| ~ coll(X4,X0,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO540+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 17:17:32 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.41 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.08/0.41 % SZS output start Saturation for theBenchmark
% See solution above
% 0.08/0.43 % Elapsed time: 0.055699 seconds
% 0.08/0.43 % CPU time: 0.234158 seconds
% 0.08/0.43 % Total memory used: 7.453 MB
% 0.08/0.43 % Net memory used: 7.164 MB
%------------------------------------------------------------------------------