SET007 Axioms: SET007+914.ax
%------------------------------------------------------------------------------
% File : SET007+914 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Circled Sets, Circled Hull, and Circled Family
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : circled1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 42 ( 2 unt; 0 def)
% Number of atoms : 468 ( 28 equ)
% Maximal formula atoms : 19 ( 11 avg)
% Number of connectives : 479 ( 53 ~; 2 |; 295 &)
% ( 9 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 10 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 5 con; 0-4 aty)
% Number of variables : 123 ( 115 !; 8 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_circled1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v3_rltopsp1(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_rltopsp1(k1_rusub_5(A,B,C),A)
& v3_rltopsp1(k1_rusub_5(A,B,C),A) ) ) ).
fof(fc2_circled1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k1_circled1(A,B)) ) ).
fof(rc1_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ? [B] :
( m1_rlvect_2(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v1_seq_1(B)
& v1_circled1(B,A) ) ) ).
fof(rc2_circled1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] :
( m2_rlvect_2(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k1_numbers)
& v1_seq_1(C)
& v1_circled1(C,A) ) ) ).
fof(t1_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v3_rltopsp1(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v3_rltopsp1(k1_rusub_5(A,B,C),A) ) ) ) ).
fof(t2_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_rltopsp1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( r1_xreal_0(k18_complex1(D),np__1)
& r2_hidden(C,B) )
=> r2_hidden(k3_rlvect_1(A,C,D),B) ) ) ) ) ) ) ).
fof(d1_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_rltopsp1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( r1_xreal_0(k18_complex1(D),np__1)
& r2_hidden(C,B) )
=> r2_hidden(k3_rlvect_1(A,C,D),B) ) ) ) ) ) ) ).
fof(t3_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( v3_rltopsp1(B,A)
=> v3_rltopsp1(k1_convex1(A,B,C),A) ) ) ) ) ).
fof(t4_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( ( v3_rltopsp1(B,A)
& v3_rltopsp1(C,A) )
=> v3_rltopsp1(k7_rusub_4(A,k1_convex1(A,B,D),k1_convex1(A,C,E)),A) ) ) ) ) ) ) ).
fof(t5_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( ( v3_rltopsp1(B,A)
& v3_rltopsp1(C,A)
& v3_rltopsp1(D,A) )
=> v3_rltopsp1(k7_rusub_4(A,k7_rusub_4(A,k1_convex1(A,B,E),k1_convex1(A,C,F)),k1_convex1(A,D,G)),A) ) ) ) ) ) ) ) ) ).
fof(t6_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> v3_rltopsp1(k3_rusub_4(A,k1_rlsub_1(A)),A) ) ).
fof(t7_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> v3_rltopsp1(k3_rusub_4(A,k2_rlsub_1(A)),A) ) ).
fof(t8_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v3_rltopsp1(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v3_rltopsp1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ).
fof(t9_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v3_rltopsp1(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v3_rltopsp1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ).
fof(d2_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( C = k1_circled1(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,C)
<=> ( v3_rltopsp1(D,A)
& r1_tarski(B,D) ) ) ) ) ) ) ) ).
fof(d3_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k2_circled1(A,B) = k6_setfam_1(u1_struct_0(A),k1_circled1(A,B)) ) ) ).
fof(t10_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,C)
=> r1_tarski(k1_circled1(A,C),k1_circled1(A,B)) ) ) ) ) ).
fof(t11_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,C)
=> r1_tarski(k2_circled1(A,B),k2_circled1(A,C)) ) ) ) ) ).
fof(t12_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(B,k2_circled1(A,B)) ) ) ).
fof(t13_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v3_rltopsp1(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_tarski(B,C)
=> r1_tarski(k2_circled1(A,B),C) ) ) ) ) ).
fof(t14_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k2_circled1(A,B) = B ) ) ).
fof(t15_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> k2_circled1(A,k1_pre_topc(A)) = k1_xboole_0 ) ).
fof(t16_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k1_convex1(A,k2_circled1(A,B),C) = k2_circled1(A,k1_convex1(A,B,C)) ) ) ) ).
fof(d4_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ( v1_circled1(B,A)
<=> ? [C] :
( m2_finseq_1(C,u1_struct_0(A))
& v2_funct_1(C)
& k2_relat_1(C) = k10_rlvect_2(A,B)
& ? [D] :
( m2_finseq_1(D,k1_numbers)
& k3_finseq_1(D) = k3_finseq_1(C)
& k15_rvsum_1(D) = np__1
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(D))
=> ( k1_funct_1(D,E) = k1_funct_1(B,k1_funct_1(C,E))
& r1_xreal_0(np__0,k1_funct_1(D,E)) ) ) ) ) ) ) ) ) ).
fof(t17_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ~ ( v1_circled1(B,A)
& k10_rlvect_2(A,B) = k1_xboole_0 ) ) ) ).
fof(t18_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( v1_circled1(B,A)
& r1_xreal_0(k8_funct_2(u1_struct_0(A),k1_numbers,B,C),np__0)
& r2_hidden(C,k10_rlvect_2(A,B)) ) ) ) ) ).
fof(t19_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ~ ( v1_circled1(B,A)
& B = k11_rlvect_2(A) ) ) ) ).
fof(t20_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ? [B] :
( m1_rlvect_2(B,A)
& v1_circled1(B,A) ) ) ).
fof(t21_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] :
( m2_rlvect_2(C,A,B)
& v1_circled1(C,A) ) ) ) ).
fof(d5_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( B = k3_circled1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ( v1_circled1(C,A)
& m1_rlvect_2(C,A) ) ) ) ) ).
fof(d6_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( C = k4_circled1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( v1_circled1(D,A)
& m2_rlvect_2(D,A,B) ) ) ) ) ) ).
fof(t22_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( v1_circled1(C,A)
& m1_rlvect_2(C,A)
& k13_rlvect_2(A,C) = B
& ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(B,D)
=> ( v1_circled1(C,A)
& m2_rlvect_2(C,A,D) ) ) ) ) ) ) ).
fof(t23_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( ( v1_circled1(D,A)
& m1_rlvect_2(D,A) )
=> ? [E] :
( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
& r1_tarski(k8_rlvect_2(A,B,C),E)
& ~ ( v1_circled1(D,A)
& m2_rlvect_2(D,A,E) ) ) ) ) ) ) ) ).
fof(t24_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v1_circled1(B,A)
& m1_rlvect_2(B,A) )
=> ! [C] :
( ( v1_circled1(C,A)
& m1_rlvect_2(C,A) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( ~ r1_xreal_0(k4_real_1(D,E),np__0)
=> k10_rlvect_2(A,k14_rlvect_2(A,k15_rlvect_2(A,D,B),k15_rlvect_2(A,E,C))) = k2_rlvect_2(A,k10_rlvect_2(A,k15_rlvect_2(A,D,B)),k10_rlvect_2(A,k15_rlvect_2(A,E,C))) ) ) ) ) ) ) ).
fof(t25_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_rlvect_2(C,A)
=> ( ( v1_circled1(C,A)
& k10_rlvect_2(A,C) = k7_rlvect_2(A,B) )
=> ( k8_funct_2(u1_struct_0(A),k1_numbers,C,B) = np__1
& k13_rlvect_2(A,C) = k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B)) ) ) ) ) ) ).
fof(t26_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_rlvect_2(D,A)
=> ( ( v1_circled1(D,A)
& k10_rlvect_2(A,D) = k8_rlvect_2(A,B,C) )
=> ( B = C
| ( k3_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,D,B),k8_funct_2(u1_struct_0(A),k1_numbers,D,C)) = np__1
& r1_xreal_0(np__0,k8_funct_2(u1_struct_0(A),k1_numbers,D,B))
& r1_xreal_0(np__0,k8_funct_2(u1_struct_0(A),k1_numbers,D,C))
& k13_rlvect_2(A,D) = k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C))) ) ) ) ) ) ) ) ).
fof(t27_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_rlvect_2(C,A,k7_rlvect_2(A,B))
=> ( v1_circled1(C,A)
=> ( k8_funct_2(u1_struct_0(A),k1_numbers,C,B) = np__1
& k13_rlvect_2(A,C) = k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B)) ) ) ) ) ) ).
fof(t28_circled1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m2_rlvect_2(D,A,k8_rlvect_2(A,B,C))
=> ( v1_circled1(D,A)
=> ( B = C
| ( k3_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,D,B),k8_funct_2(u1_struct_0(A),k1_numbers,D,C)) = np__1
& r1_xreal_0(np__0,k8_funct_2(u1_struct_0(A),k1_numbers,D,B))
& r1_xreal_0(np__0,k8_funct_2(u1_struct_0(A),k1_numbers,D,C))
& k13_rlvect_2(A,D) = k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C))) ) ) ) ) ) ) ) ).
fof(dt_k1_circled1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k1_circled1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_circled1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_rltopsp1(k2_circled1(A,B),A)
& m1_subset_1(k2_circled1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(dt_k3_circled1,axiom,
$true ).
fof(dt_k4_circled1,axiom,
$true ).
%------------------------------------------------------------------------------