SET007 Axioms: SET007+413.ax
%------------------------------------------------------------------------------
% File : SET007+413 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Minimization of Finite State Machines
% 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 : fsm_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 167 ( 9 unt; 0 def)
% Number of atoms : 1452 ( 147 equ)
% Maximal formula atoms : 26 ( 8 avg)
% Number of connectives : 1741 ( 456 ~; 1 |; 604 &)
% ( 32 <=>; 648 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 12 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 43 ( 41 usr; 1 prp; 0-6 aty)
% Number of functors : 50 ( 50 usr; 4 con; 0-6 aty)
% Number of variables : 773 ( 742 !; 31 ?)
% 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(cc1_fsm_1,axiom,
! [A] :
( v1_finset_1(A)
=> ! [B] :
( m1_eqrel_1(B,A)
=> ( v1_finset_1(B)
& v1_setfam_1(B) ) ) ) ).
fof(rc1_fsm_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ? [B] :
( m1_eqrel_1(B,A)
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_setfam_1(B) ) ) ).
fof(rc2_fsm_1,axiom,
! [A] :
? [B] :
( l1_fsm_1(B,A)
& v1_fsm_1(B,A) ) ).
fof(rc3_fsm_1,axiom,
! [A] :
? [B] :
( l1_fsm_1(B,A)
& ~ v3_struct_0(B)
& v6_group_1(B) ) ).
fof(rc4_fsm_1,axiom,
? [A] :
( l1_struct_0(A)
& ~ v3_struct_0(A)
& v6_group_1(A) ) ).
fof(fc1_fsm_1,axiom,
! [A] :
( ( v6_group_1(A)
& l1_struct_0(A) )
=> v1_finset_1(u1_struct_0(A)) ) ).
fof(rc5_fsm_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ? [C] :
( l2_fsm_1(C,A,B)
& v2_fsm_1(C,A,B) ) ) ).
fof(rc6_fsm_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ? [C] :
( l3_fsm_1(C,A,B)
& v3_fsm_1(C,A,B) ) ) ).
fof(fc2_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,A),B)
& m1_relset_1(C,k2_zfmisc_1(B,A),B)
& m1_subset_1(D,B) )
=> ( ~ v3_struct_0(g1_fsm_1(A,B,C,D))
& v6_group_1(g1_fsm_1(A,B,C,D))
& v1_fsm_1(g1_fsm_1(A,B,C,D),A) ) ) ).
fof(fc3_fsm_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_finset_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,A),C)
& m1_relset_1(D,k2_zfmisc_1(C,A),C)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(C,A),B)
& m1_relset_1(E,k2_zfmisc_1(C,A),B)
& m1_subset_1(F,C) )
=> ( ~ v3_struct_0(g2_fsm_1(A,B,C,D,E,F))
& v6_group_1(g2_fsm_1(A,B,C,D,E,F))
& v2_fsm_1(g2_fsm_1(A,B,C,D,E,F),A,B) ) ) ).
fof(fc4_fsm_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_finset_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,A),C)
& m1_relset_1(D,k2_zfmisc_1(C,A),C)
& v1_funct_1(E)
& v1_funct_2(E,C,B)
& m1_relset_1(E,C,B)
& m1_subset_1(F,C) )
=> ( ~ v3_struct_0(g3_fsm_1(A,B,C,D,E,F))
& v6_group_1(g3_fsm_1(A,B,C,D,E,F))
& v3_fsm_1(g3_fsm_1(A,B,C,D,E,F),A,B) ) ) ).
fof(rc7_fsm_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ? [C] :
( l2_fsm_1(C,A,B)
& ~ v3_struct_0(C)
& v6_group_1(C) ) ) ).
fof(rc8_fsm_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ? [C] :
( l3_fsm_1(C,A,B)
& ~ v3_struct_0(C)
& v6_group_1(C) ) ) ).
fof(fc5_fsm_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ( ~ v3_struct_0(k11_fsm_1(A,B,C))
& v6_group_1(k11_fsm_1(A,B,C))
& v2_fsm_1(k11_fsm_1(A,B,C),A,B) ) ) ).
fof(rc9_fsm_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ? [C] :
( l2_fsm_1(C,A,B)
& ~ v3_struct_0(C)
& v6_group_1(C)
& v5_fsm_1(C,A,B) ) ) ).
fof(rc10_fsm_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ? [C] :
( l2_fsm_1(C,A,B)
& ~ v3_struct_0(C)
& v6_group_1(C)
& v7_fsm_1(C,A,B) ) ) ).
fof(rc11_fsm_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ? [C] :
( l2_fsm_1(C,A,B)
& ~ v3_struct_0(C)
& v6_group_1(C)
& v5_fsm_1(C,A,B)
& v7_fsm_1(C,A,B) ) ) ).
fof(fc6_fsm_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ( ~ v1_xboole_0(k12_fsm_1(A,B,C))
& v1_finset_1(k12_fsm_1(A,B,C)) ) ) ).
fof(fc7_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B)
& ~ v3_struct_0(D)
& v6_group_1(D)
& l2_fsm_1(D,A,B) )
=> ( ~ v3_struct_0(k13_fsm_1(A,B,C,D))
& v6_group_1(k13_fsm_1(A,B,C,D))
& v2_fsm_1(k13_fsm_1(A,B,C,D),A,B) ) ) ).
fof(t1_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( B = k1_nat_1(A,C)
& r1_xreal_0(np__1,C) ) ) ) ) ) ).
fof(t2_fsm_1,axiom,
$true ).
fof(t3_fsm_1,axiom,
$true ).
fof(t4_fsm_1,axiom,
$true ).
fof(t5_fsm_1,axiom,
$true ).
fof(t6_fsm_1,axiom,
$true ).
fof(t7_fsm_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,C)
& m2_relset_1(E,B,C) )
=> ( ( v3_funct_2(D,A,B)
& v3_funct_2(E,B,C) )
=> v3_funct_2(k7_funct_2(A,B,C,D,E),A,C) ) ) ) ) ) ).
fof(t8_fsm_1,axiom,
! [A,B] :
( ( v3_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v3_relat_2(C)
& v8_relat_2(C)
& v1_partfun1(C,A,A)
& m2_relset_1(C,A,A) )
=> ( k8_eqrel_1(A,B) = k8_eqrel_1(A,C)
=> B = C ) ) ) ).
fof(t9_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_eqrel_1(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(t10_fsm_1,axiom,
! [A] :
( v1_finset_1(A)
=> ! [B] :
( m1_eqrel_1(B,A)
=> v1_finset_1(B) ) ) ).
fof(t11_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_eqrel_1(B,A)
=> ! [C] :
~ ( r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,A)
=> ~ r2_hidden(D,C) ) ) ) ) ).
fof(t12_fsm_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m1_eqrel_1(B,A)
=> r1_xreal_0(k4_card_1(B),k4_card_1(A)) ) ) ).
fof(t13_fsm_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m1_eqrel_1(B,A)
=> ! [C] :
( m1_eqrel_1(C,A)
=> ( r1_setfam_1(B,C)
=> r1_xreal_0(k4_card_1(C),k4_card_1(B)) ) ) ) ) ).
fof(t14_fsm_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m1_eqrel_1(B,A)
=> ! [C] :
( m1_eqrel_1(C,A)
=> ( r1_setfam_1(B,C)
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),C)
=> ? [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
& r1_tarski(E,D) ) ) ) ) ) ) ).
fof(t15_fsm_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A) )
=> ! [B] :
( m1_eqrel_1(B,A)
=> ! [C] :
( m1_eqrel_1(C,A)
=> ( ( r1_setfam_1(B,C)
& k4_card_1(B) = k4_card_1(C) )
=> B = C ) ) ) ) ).
fof(d1_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k1_fsm_1(A,B,C,D) = k8_funct_2(k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B),u1_fsm_1(A,B),k1_domain_1(u1_struct_0(B),A,D,C)) ) ) ) ) ).
fof(d2_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(B))
=> ( E = k2_fsm_1(A,B,C,D)
<=> ( k1_funct_1(E,np__1) = C
& k3_finseq_1(E) = k1_nat_1(k3_finseq_1(D),np__1)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,F)
& r1_xreal_0(F,k3_finseq_1(D))
& ! [G] :
( m1_subset_1(G,A)
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(B))
=> ~ ( G = k1_funct_1(D,F)
& H = k1_funct_1(E,F)
& I = k1_funct_1(E,k1_nat_1(F,np__1))
& k1_fsm_1(A,B,G,H) = I ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k2_fsm_1(A,B,C,k6_finseq_1(A)) = k4_matrix_2(u1_struct_0(B),C) ) ) ) ).
fof(d3_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_fsm_1(A,B,C,D,E)
<=> k1_funct_1(k2_fsm_1(A,B,D,C),k1_nat_1(k3_finseq_1(C),np__1)) = E ) ) ) ) ) ) ).
fof(t17_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> r1_fsm_1(A,B,k6_finseq_1(A),C,C) ) ) ) ).
fof(d4_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(B))
=> ( r2_fsm_1(A,B,C,D)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& E = k1_funct_1(D,np__1)
& k2_fsm_1(A,B,E,C) = D ) ) ) ) ) ) ).
fof(t18_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> r2_fsm_1(A,B,k6_finseq_1(A),k4_matrix_2(u1_struct_0(B),C)) ) ) ) ).
fof(d5_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( E = k3_fsm_1(A,B,C,D)
<=> r1_fsm_1(A,B,D,C,E) ) ) ) ) ) ) ).
fof(t19_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( k1_funct_1(k2_fsm_1(A,B,D,C),k3_finseq_1(k2_fsm_1(A,B,D,C))) = E
<=> r1_fsm_1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t20_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,F)
& r1_xreal_0(F,k3_finseq_1(C)) )
=> k1_funct_1(k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)),F) = k1_funct_1(k2_fsm_1(A,B,E,C),F) ) ) ) ) ) ) ) ).
fof(t21_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_fsm_1(A,B,C,E,F)
=> k1_funct_1(k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)),k1_nat_1(k3_finseq_1(C),np__1)) = F ) ) ) ) ) ) ) ).
fof(t22_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_fsm_1(A,B,C,E,F)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,G)
& r1_xreal_0(G,k1_nat_1(k3_finseq_1(D),np__1)) )
=> k1_funct_1(k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)),k1_nat_1(k3_finseq_1(C),G)) = k1_funct_1(k2_fsm_1(A,B,F,D),G) ) ) ) ) ) ) ) ) ) ).
fof(t23_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_fsm_1(A,B,C,E,F)
=> k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)) = k7_finseq_1(k2_finseq_3(k1_nat_1(k3_finseq_1(C),np__1),k2_fsm_1(A,B,E,C)),k2_fsm_1(A,B,F,D)) ) ) ) ) ) ) ) ).
fof(d6_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m2_finseq_1(E,A)
=> ! [F] :
( m2_finseq_1(F,B)
=> ( F = k4_fsm_1(A,B,C,D,E)
<=> ( k3_finseq_1(F) = k3_finseq_1(E)
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r2_hidden(G,k4_finseq_1(E))
=> k1_funct_1(F,G) = k1_funct_1(u3_fsm_1(A,B,C),k4_tarski(k1_funct_1(k2_fsm_1(A,C,D,E),G),k1_funct_1(E,G))) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> k4_fsm_1(A,B,C,D,k6_finseq_1(A)) = k6_finseq_1(B) ) ) ) ) ).
fof(d7_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l3_fsm_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m2_finseq_1(E,A)
=> ! [F] :
( m2_finseq_1(F,B)
=> ( F = k5_fsm_1(A,B,C,D,E)
<=> ( k3_finseq_1(F) = k1_nat_1(k3_finseq_1(E),np__1)
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r2_hidden(G,k2_finseq_1(k1_nat_1(k3_finseq_1(E),np__1)))
=> k1_funct_1(F,G) = k1_funct_1(u4_fsm_1(A,B,C),k1_funct_1(k2_fsm_1(A,C,D,E),G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l3_fsm_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> k1_funct_1(k5_fsm_1(A,B,D,E,C),np__1) = k8_funct_2(u1_struct_0(D),B,u4_fsm_1(A,B,D),E) ) ) ) ) ) ).
fof(t26_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(E))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(E))
=> ( r1_fsm_1(A,E,C,F,G)
=> k4_fsm_1(A,B,E,F,k8_finseq_1(A,C,D)) = k8_finseq_1(B,k4_fsm_1(A,B,E,F,C),k4_fsm_1(A,B,E,G,D)) ) ) ) ) ) ) ) ) ).
fof(t27_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& l2_fsm_1(F,A,B) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(E))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(E))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(F))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(F))
=> ~ ( r1_fsm_1(A,E,C,G,H)
& r1_fsm_1(A,F,C,I,J)
& k4_fsm_1(A,B,E,H,D) != k4_fsm_1(A,B,F,J,D)
& k4_fsm_1(A,B,E,G,k8_finseq_1(A,C,D)) = k4_fsm_1(A,B,F,I,k8_finseq_1(A,C,D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l3_fsm_1(D,A,B) )
=> ( r3_fsm_1(A,B,C,D)
<=> ! [E] :
( m2_finseq_1(E,A)
=> k8_finseq_1(B,k4_matrix_2(B,k8_funct_2(u1_struct_0(D),B,u4_fsm_1(A,B,D),u2_fsm_1(A,D))),k4_fsm_1(A,B,C,u2_fsm_1(A,C),E)) = k5_fsm_1(A,B,D,u2_fsm_1(A,D),E) ) ) ) ) ) ) ).
fof(t28_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l3_fsm_1(C,A,B) )
=> ? [D] :
( ~ v3_struct_0(D)
& v6_group_1(D)
& l2_fsm_1(D,A,B)
& r3_fsm_1(A,B,D,C) ) ) ) ) ).
fof(t29_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ? [D] :
( ~ v3_struct_0(D)
& v6_group_1(D)
& l3_fsm_1(D,A,B)
& r3_fsm_1(A,B,C,D) ) ) ) ) ).
fof(d9_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ( r4_fsm_1(A,B,C,D)
<=> ! [E] :
( m2_finseq_1(E,A)
=> k4_fsm_1(A,B,C,u2_fsm_1(A,C),E) = k4_fsm_1(A,B,D,u2_fsm_1(A,D),E) ) ) ) ) ) ) ).
fof(t30_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,A,B) )
=> ( ( r4_fsm_1(A,B,C,D)
& r4_fsm_1(A,B,D,E) )
=> r4_fsm_1(A,B,C,E) ) ) ) ) ) ) ).
fof(d10_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( r5_fsm_1(A,B,C,D,E)
<=> ! [F] :
( m2_finseq_1(F,A)
=> k4_fsm_1(A,B,C,D,F) = k4_fsm_1(A,B,C,E,F) ) ) ) ) ) ) ) ).
fof(t31_fsm_1,axiom,
$true ).
fof(t32_fsm_1,axiom,
$true ).
fof(t33_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ( ( r5_fsm_1(A,B,C,D,E)
& r5_fsm_1(A,B,C,E,F) )
=> r5_fsm_1(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(t34_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(E))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(E))
=> ( F = k8_funct_2(k2_zfmisc_1(u1_struct_0(E),A),u1_struct_0(E),u1_fsm_1(A,E),k1_domain_1(u1_struct_0(E),A,G,C))
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( r2_hidden(H,k2_finseq_1(k1_nat_1(k3_finseq_1(D),np__1)))
=> k1_funct_1(k2_fsm_1(A,E,G,k8_finseq_1(A,k4_matrix_2(A,C),D)),k1_nat_1(H,np__1)) = k1_funct_1(k2_fsm_1(A,E,F,D),H) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(E))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(E))
=> ( F = k8_funct_2(k2_zfmisc_1(u1_struct_0(E),A),u1_struct_0(E),u1_fsm_1(A,E),k1_domain_1(u1_struct_0(E),A,G,C))
=> k4_fsm_1(A,B,E,G,k8_finseq_1(A,k4_matrix_2(A,C),D)) = k8_finseq_1(B,k4_matrix_2(B,k8_funct_2(k2_zfmisc_1(u1_struct_0(E),A),B,u3_fsm_1(A,B,E),k1_domain_1(u1_struct_0(E),A,G,C))),k4_fsm_1(A,B,E,F,D)) ) ) ) ) ) ) ) ) ).
fof(t36_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,B,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( r5_fsm_1(B,A,C,D,E)
<=> ! [F] :
( m1_subset_1(F,B)
=> ( k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),A,u3_fsm_1(B,A,C),k1_domain_1(u1_struct_0(C),B,D,F)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),A,u3_fsm_1(B,A,C),k1_domain_1(u1_struct_0(C),B,E,F))
& r5_fsm_1(B,A,C,k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k1_domain_1(u1_struct_0(C),B,D,F)),k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k1_domain_1(u1_struct_0(C),B,E,F))) ) ) ) ) ) ) ) ) ).
fof(t37_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,B,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( r5_fsm_1(B,A,C,D,E)
=> ! [F] :
( m2_finseq_1(F,B)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(G,k4_finseq_1(F))
& ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(C))
=> ~ ( H = k1_funct_1(k2_fsm_1(B,C,D,F),G)
& I = k1_funct_1(k2_fsm_1(B,C,E,F),G)
& r5_fsm_1(B,A,C,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d11_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r6_fsm_1(A,B,C,D,E,F)
<=> ! [G] :
( m2_finseq_1(G,A)
=> ( r1_xreal_0(k3_finseq_1(G),F)
=> k4_fsm_1(A,B,C,D,G) = k4_fsm_1(A,B,C,E,G) ) ) ) ) ) ) ) ) ) ).
fof(t38_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> r6_fsm_1(B,C,D,E,E,A) ) ) ) ) ) ).
fof(t39_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( r6_fsm_1(B,C,D,E,F,A)
=> r6_fsm_1(B,C,D,F,E,A) ) ) ) ) ) ) ) ).
fof(t40_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ( ( r6_fsm_1(B,C,D,E,F,A)
& r6_fsm_1(B,C,D,F,G,A) )
=> r6_fsm_1(B,C,D,E,G,A) ) ) ) ) ) ) ) ) ).
fof(t41_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( r5_fsm_1(B,C,D,E,F)
=> r6_fsm_1(B,C,D,E,F,A) ) ) ) ) ) ) ) ).
fof(t42_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> r6_fsm_1(A,B,C,D,E,np__0) ) ) ) ) ) ).
fof(t43_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,C,D) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(E))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(E))
=> ( r6_fsm_1(C,D,E,F,G,k1_nat_1(A,B))
=> r6_fsm_1(C,D,E,F,G,A) ) ) ) ) ) ) ) ) ).
fof(t44_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,C,B) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( r1_xreal_0(np__1,A)
=> ( r6_fsm_1(C,B,D,E,F,A)
<=> ( r6_fsm_1(C,B,D,E,F,np__1)
& ! [G] :
( m1_subset_1(G,C)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( H = k6_xcmplx_0(A,np__1)
=> r6_fsm_1(C,B,D,k8_funct_2(k2_zfmisc_1(u1_struct_0(D),C),u1_struct_0(D),u1_fsm_1(C,D),k1_domain_1(u1_struct_0(D),C,E,G)),k8_funct_2(k2_zfmisc_1(u1_struct_0(D),C),u1_struct_0(D),u1_fsm_1(C,D),k1_domain_1(u1_struct_0(D),C,F,G)),H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d12_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v3_relat_2(E)
& v8_relat_2(E)
& v1_partfun1(E,u1_struct_0(C),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(C)) )
=> ( E = k6_fsm_1(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( r2_hidden(k1_domain_1(u1_struct_0(C),u1_struct_0(C),F,G),E)
<=> r6_fsm_1(A,B,C,F,G,D) ) ) ) ) ) ) ) ) ) ).
fof(d13_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k7_fsm_1(A,B,C,D) = k8_eqrel_1(u1_struct_0(C),k6_fsm_1(A,B,C,D)) ) ) ) ) ).
fof(t45_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> r1_setfam_1(k7_fsm_1(B,C,D,k1_nat_1(A,np__1)),k7_fsm_1(B,C,D,A)) ) ) ) ) ).
fof(t46_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> ( k8_eqrel_1(u1_struct_0(D),k6_fsm_1(B,C,D,A)) = k8_eqrel_1(u1_struct_0(D),k6_fsm_1(B,C,D,k1_nat_1(A,np__1)))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k8_eqrel_1(u1_struct_0(D),k6_fsm_1(B,C,D,k1_nat_1(A,E))) = k8_eqrel_1(u1_struct_0(D),k6_fsm_1(B,C,D,A)) ) ) ) ) ) ) ).
fof(t47_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> ( k7_fsm_1(B,C,D,A) = k7_fsm_1(B,C,D,k1_nat_1(A,np__1))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k7_fsm_1(B,C,D,k1_nat_1(A,E)) = k7_fsm_1(B,C,D,A) ) ) ) ) ) ) ).
fof(t48_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> ( k7_fsm_1(B,C,D,k1_nat_1(A,np__1)) != k7_fsm_1(B,C,D,A)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(E,A)
& k7_fsm_1(B,C,D,k1_nat_1(E,np__1)) = k7_fsm_1(B,C,D,E) ) ) ) ) ) ) ) ).
fof(t49_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& l2_fsm_1(D,B,C) )
=> ~ ( k7_fsm_1(B,C,D,A) != k7_fsm_1(B,C,D,k1_nat_1(A,np__1))
& r1_xreal_0(k4_card_1(k7_fsm_1(B,C,D,k1_nat_1(A,np__1))),k4_card_1(k7_fsm_1(B,C,D,A))) ) ) ) ) ) ).
fof(t50_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> k6_eqrel_1(u1_struct_0(C),k6_fsm_1(A,B,C,np__0),D) = u1_struct_0(C) ) ) ) ) ).
fof(t51_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> k7_fsm_1(A,B,C,np__0) = k1_tarski(u1_struct_0(C)) ) ) ) ).
fof(t52_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& l2_fsm_1(D,B,C) )
=> ( k1_nat_1(A,np__1) = k4_card_1(u1_struct_0(D))
=> k7_fsm_1(B,C,D,k1_nat_1(A,np__1)) = k7_fsm_1(B,C,D,A) ) ) ) ) ) ).
fof(d14_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m1_eqrel_1(D,u1_struct_0(C))
=> ( v4_fsm_1(D,A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ( r5_fsm_1(A,B,C,E,F)
<=> ? [G] :
( m2_subset_1(G,k1_zfmisc_1(u1_struct_0(C)),D)
& r2_hidden(E,G)
& r2_hidden(F,G) ) ) ) ) ) ) ) ) ) ).
fof(t53_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> ( v4_fsm_1(k7_fsm_1(B,C,D,A),B,C,D)
=> k6_fsm_1(B,C,D,k1_nat_1(A,np__1)) = k6_fsm_1(B,C,D,A) ) ) ) ) ) ).
fof(t54_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> ( k7_fsm_1(B,C,D,A) = k7_fsm_1(B,C,D,k1_nat_1(A,np__1))
<=> v4_fsm_1(k7_fsm_1(B,C,D,A),B,C,D) ) ) ) ) ) ).
fof(t55_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& l2_fsm_1(D,B,C) )
=> ~ ( k1_nat_1(A,np__1) = k4_card_1(u1_struct_0(D))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(E,A)
& v4_fsm_1(k7_fsm_1(B,C,D,E),B,C,D) ) ) ) ) ) ) ) ).
fof(d15_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m1_eqrel_1(D,u1_struct_0(C))
=> ( D = k8_fsm_1(A,B,C)
<=> v4_fsm_1(D,A,B,C) ) ) ) ) ) ).
fof(t56_fsm_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& l2_fsm_1(D,B,C) )
=> ( k1_nat_1(A,np__1) = k4_card_1(u1_struct_0(D))
=> k8_fsm_1(B,C,D) = k7_fsm_1(B,C,D,A) ) ) ) ) ) ).
fof(d16_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(C)),k8_fsm_1(A,B,C))
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m2_subset_1(F,k1_zfmisc_1(u1_struct_0(C)),k8_fsm_1(A,B,C))
=> ( F = k9_fsm_1(A,B,C,D,E)
<=> ? [G] :
( m1_subset_1(G,u1_struct_0(C))
& ? [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
& r2_hidden(G,D)
& k1_nat_1(H,np__1) = k4_card_1(u1_struct_0(C))
& F = k6_eqrel_1(u1_struct_0(C),k6_fsm_1(A,B,C,H),k8_funct_2(k2_zfmisc_1(u1_struct_0(C),A),u1_struct_0(C),u1_fsm_1(A,C),k1_domain_1(u1_struct_0(C),A,G,E))) ) ) ) ) ) ) ) ) ) ).
fof(d17_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(C)),k8_fsm_1(A,B,C))
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,B)
=> ( F = k10_fsm_1(A,B,C,D,E)
<=> ? [G] :
( m1_subset_1(G,u1_struct_0(C))
& r2_hidden(G,D)
& F = k8_funct_2(k2_zfmisc_1(u1_struct_0(C),A),B,u3_fsm_1(A,B,C),k1_domain_1(u1_struct_0(C),A,G,E)) ) ) ) ) ) ) ) ) ).
fof(d18_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( v2_fsm_1(D,A,B)
& l2_fsm_1(D,A,B) )
=> ( D = k11_fsm_1(A,B,C)
<=> ( u1_struct_0(D) = k8_fsm_1(A,B,C)
& ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( r2_hidden(G,E)
=> ( r2_hidden(k8_funct_2(k2_zfmisc_1(u1_struct_0(C),A),u1_struct_0(C),u1_fsm_1(A,C),k1_domain_1(u1_struct_0(C),A,G,F)),k1_funct_1(u1_fsm_1(A,D),k4_tarski(E,F)))
& k8_funct_2(k2_zfmisc_1(u1_struct_0(C),A),B,u3_fsm_1(A,B,C),k1_domain_1(u1_struct_0(C),A,G,F)) = k1_funct_1(u3_fsm_1(A,B,D),k4_tarski(E,F)) ) ) ) ) )
& r2_hidden(u2_fsm_1(A,C),u2_fsm_1(A,D)) ) ) ) ) ) ) ).
fof(t57_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v6_group_1(E)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(E))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ( ( D = k11_fsm_1(A,B,E)
& r2_hidden(F,G) )
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( r2_hidden(H,k2_finseq_1(k1_nat_1(k3_finseq_1(C),np__1)))
=> r2_hidden(k1_funct_1(k2_fsm_1(A,E,F,C),H),k1_funct_1(k2_fsm_1(A,D,G,C),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t58_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> r4_fsm_1(A,B,C,k11_fsm_1(A,B,C)) ) ) ) ).
fof(d19_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ( r7_fsm_1(A,B,C,D)
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(D))
& v3_funct_2(E,u1_struct_0(C),u1_struct_0(D))
& k8_funct_2(u1_struct_0(C),u1_struct_0(D),E,u2_fsm_1(A,C)) = u2_fsm_1(A,D)
& ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,A)
=> ( k8_funct_2(u1_struct_0(C),u1_struct_0(D),E,k8_funct_2(k2_zfmisc_1(u1_struct_0(C),A),u1_struct_0(C),u1_fsm_1(A,C),k1_domain_1(u1_struct_0(C),A,F,G))) = k8_funct_2(k2_zfmisc_1(u1_struct_0(D),A),u1_struct_0(D),u1_fsm_1(A,D),k1_domain_1(u1_struct_0(D),A,k8_funct_2(u1_struct_0(C),u1_struct_0(D),E,F),G))
& k8_funct_2(k2_zfmisc_1(u1_struct_0(C),A),B,u3_fsm_1(A,B,C),k1_domain_1(u1_struct_0(C),A,F,G)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(D),A),B,u3_fsm_1(A,B,D),k1_domain_1(u1_struct_0(D),A,k8_funct_2(u1_struct_0(C),u1_struct_0(D),E,F),G)) ) ) ) ) ) ) ) ) ) ).
fof(t59_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,A,B) )
=> ( ( r7_fsm_1(A,B,C,D)
& r7_fsm_1(A,B,D,E) )
=> r7_fsm_1(A,B,C,E) ) ) ) ) ) ) ).
fof(t60_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,B)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,B,A) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) )
=> ( ! [H] :
( m1_subset_1(H,u1_struct_0(D))
=> ! [I] :
( m1_subset_1(I,B)
=> k8_funct_2(u1_struct_0(D),u1_struct_0(E),G,k8_funct_2(k2_zfmisc_1(u1_struct_0(D),B),u1_struct_0(D),u1_fsm_1(B,D),k1_domain_1(u1_struct_0(D),B,H,I))) = k8_funct_2(k2_zfmisc_1(u1_struct_0(E),B),u1_struct_0(E),u1_fsm_1(B,E),k1_domain_1(u1_struct_0(E),B,k8_funct_2(u1_struct_0(D),u1_struct_0(E),G,H),I)) ) )
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,H)
& r1_xreal_0(H,k1_nat_1(k3_finseq_1(C),np__1)) )
=> k1_funct_1(G,k1_funct_1(k2_fsm_1(B,D,F,C),H)) = k1_funct_1(k2_fsm_1(B,E,k8_funct_2(u1_struct_0(D),u1_struct_0(E),G,F),C),H) ) ) ) ) ) ) ) ) ) ) ).
fof(t61_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,B,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,B,A) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(G,u1_struct_0(C),u1_struct_0(D)) )
=> ( ( k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,u2_fsm_1(B,C)) = u2_fsm_1(B,D)
& ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ! [I] :
( m1_subset_1(I,B)
=> ( k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k1_domain_1(u1_struct_0(C),B,H,I))) = k8_funct_2(k2_zfmisc_1(u1_struct_0(D),B),u1_struct_0(D),u1_fsm_1(B,D),k1_domain_1(u1_struct_0(D),B,k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,H),I))
& k8_funct_2(k2_zfmisc_1(u1_struct_0(C),B),A,u3_fsm_1(B,A,C),k1_domain_1(u1_struct_0(C),B,H,I)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(D),B),A,u3_fsm_1(B,A,D),k1_domain_1(u1_struct_0(D),B,k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,H),I)) ) ) ) )
=> ( r5_fsm_1(B,A,C,E,F)
<=> r5_fsm_1(B,A,D,k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,E),k8_funct_2(u1_struct_0(C),u1_struct_0(D),G,F)) ) ) ) ) ) ) ) ) ) ).
fof(t62_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ~ ( C = k11_fsm_1(A,B,D)
& E != F
& r5_fsm_1(A,B,C,E,F) ) ) ) ) ) ) ) ).
fof(d20_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ( v5_fsm_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ~ ( D != E
& r5_fsm_1(A,B,C,D,E) ) ) ) ) ) ) ) ).
fof(t63_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> v5_fsm_1(k11_fsm_1(A,B,C),A,B) ) ) ) ).
fof(t64_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& v5_fsm_1(C,A,B)
& l2_fsm_1(C,A,B) )
=> r7_fsm_1(A,B,C,k11_fsm_1(A,B,C)) ) ) ) ).
fof(t65_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ( v5_fsm_1(C,A,B)
<=> ? [D] :
( ~ v3_struct_0(D)
& v6_group_1(D)
& l2_fsm_1(D,A,B)
& r7_fsm_1(A,B,C,k11_fsm_1(A,B,D)) ) ) ) ) ) ).
fof(d21_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( v6_fsm_1(D,A,B,C)
<=> ? [E] :
( m2_finseq_1(E,A)
& r1_fsm_1(A,C,E,u2_fsm_1(A,C),D) ) ) ) ) ) ) ).
fof(d22_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ( v7_fsm_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> v6_fsm_1(D,A,B,C) ) ) ) ) ) ).
fof(t66_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& v7_fsm_1(C,A,B)
& l2_fsm_1(C,A,B) )
=> v7_fsm_1(k11_fsm_1(A,B,C),A,B) ) ) ) ).
fof(t67_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,B,A) )
=> ( r1_tarski(k12_fsm_1(B,A,C),u1_struct_0(C))
& ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( r2_hidden(D,k12_fsm_1(B,A,C))
<=> v6_fsm_1(D,B,A,C) ) ) ) ) ) ) ).
fof(t68_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,B,A) )
=> ( v1_funct_1(k2_partfun1(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k2_zfmisc_1(k12_fsm_1(B,A,C),B)))
& v1_funct_2(k2_partfun1(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k2_zfmisc_1(k12_fsm_1(B,A,C),B)),k2_zfmisc_1(k12_fsm_1(B,A,C),B),k12_fsm_1(B,A,C))
& m2_relset_1(k2_partfun1(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k2_zfmisc_1(k12_fsm_1(B,A,C),B)),k2_zfmisc_1(k12_fsm_1(B,A,C),B),k12_fsm_1(B,A,C)) ) ) ) ) ).
fof(t69_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k12_fsm_1(A,B,C),A),k12_fsm_1(A,B,C))
& m2_relset_1(D,k2_zfmisc_1(k12_fsm_1(A,B,C),A),k12_fsm_1(A,B,C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(k12_fsm_1(A,B,C),A),B)
& m2_relset_1(E,k2_zfmisc_1(k12_fsm_1(A,B,C),A),B) )
=> ! [F] :
( m1_subset_1(F,k12_fsm_1(A,B,C))
=> ( ( D = k2_partfun1(k2_zfmisc_1(u1_struct_0(C),A),u1_struct_0(C),u1_fsm_1(A,C),k2_zfmisc_1(k12_fsm_1(A,B,C),A))
& E = k2_partfun1(k2_zfmisc_1(u1_struct_0(C),A),B,u3_fsm_1(A,B,C),k2_zfmisc_1(k12_fsm_1(A,B,C),A))
& F = u2_fsm_1(A,C) )
=> r4_fsm_1(A,B,C,g2_fsm_1(A,B,k12_fsm_1(A,B,C),D,E,F)) ) ) ) ) ) ) ) ).
fof(t70_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,B,A) )
=> ? [D] :
( ~ v3_struct_0(D)
& v6_group_1(D)
& v7_fsm_1(D,B,A)
& l2_fsm_1(D,B,A)
& u1_fsm_1(B,D) = k2_partfun1(k2_zfmisc_1(u1_struct_0(C),B),u1_struct_0(C),u1_fsm_1(B,C),k2_zfmisc_1(k12_fsm_1(B,A,C),B))
& u3_fsm_1(B,A,D) = k2_partfun1(k2_zfmisc_1(u1_struct_0(C),B),A,u3_fsm_1(B,A,C),k2_zfmisc_1(k12_fsm_1(B,A,C),B))
& u2_fsm_1(B,D) = u2_fsm_1(B,C)
& r4_fsm_1(B,A,C,D) ) ) ) ) ).
fof(d24_fsm_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( v2_fsm_1(E,A,B)
& l2_fsm_1(E,A,B) )
=> ( E = k13_fsm_1(A,B,C,D)
<=> ( u1_struct_0(E) = k2_xboole_0(u1_struct_0(C),u1_struct_0(D))
& u1_fsm_1(A,E) = k1_funct_4(u1_fsm_1(A,C),u1_fsm_1(A,D))
& u3_fsm_1(A,B,E) = k1_funct_4(u3_fsm_1(A,B,C),u3_fsm_1(A,B,D))
& u2_fsm_1(A,E) = u2_fsm_1(A,C) ) ) ) ) ) ) ).
fof(t71_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ! [G] :
( ( ~ v3_struct_0(G)
& v6_group_1(G)
& l2_fsm_1(G,A,B) )
=> ! [H] :
( m1_subset_1(H,u1_struct_0(G))
=> ( ( G = k13_fsm_1(A,B,D,E)
& r1_subset_1(u1_struct_0(D),u1_struct_0(E))
& F = H )
=> k2_fsm_1(A,D,F,C) = k2_fsm_1(A,G,H,C) ) ) ) ) ) ) ) ) ) ).
fof(t72_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ! [G] :
( ( ~ v3_struct_0(G)
& v6_group_1(G)
& l2_fsm_1(G,A,B) )
=> ! [H] :
( m1_subset_1(H,u1_struct_0(G))
=> ( ( G = k13_fsm_1(A,B,D,E)
& r1_subset_1(u1_struct_0(D),u1_struct_0(E))
& F = H )
=> k4_fsm_1(A,B,D,F,C) = k4_fsm_1(A,B,G,H,C) ) ) ) ) ) ) ) ) ) ).
fof(t73_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(E))
=> ! [G] :
( ( ~ v3_struct_0(G)
& v6_group_1(G)
& l2_fsm_1(G,A,B) )
=> ! [H] :
( m1_subset_1(H,u1_struct_0(G))
=> ( ( G = k13_fsm_1(A,B,D,E)
& r1_subset_1(u1_struct_0(D),u1_struct_0(E))
& F = H )
=> k2_fsm_1(A,E,F,C) = k2_fsm_1(A,G,H,C) ) ) ) ) ) ) ) ) ) ).
fof(t74_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(E))
=> ! [G] :
( ( ~ v3_struct_0(G)
& v6_group_1(G)
& l2_fsm_1(G,A,B) )
=> ! [H] :
( m1_subset_1(H,u1_struct_0(G))
=> ( ( G = k13_fsm_1(A,B,D,E)
& r1_subset_1(u1_struct_0(D),u1_struct_0(E))
& F = H )
=> k4_fsm_1(A,B,E,F,C) = k4_fsm_1(A,B,G,H,C) ) ) ) ) ) ) ) ) ) ).
fof(t75_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v5_fsm_1(D,A,B)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v5_fsm_1(E,A,B)
& l2_fsm_1(E,A,B) )
=> ~ ( C = k13_fsm_1(A,B,D,E)
& r1_subset_1(u1_struct_0(D),u1_struct_0(E))
& r4_fsm_1(A,B,D,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C)))
=> ~ ( r2_hidden(u2_fsm_1(A,D),F)
& r2_hidden(u2_fsm_1(A,E),F)
& F = u2_fsm_1(A,k11_fsm_1(A,B,C)) ) ) ) ) ) ) ) ) ).
fof(t76_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v5_fsm_1(D,A,B)
& v7_fsm_1(D,A,B)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v5_fsm_1(E,A,B)
& v7_fsm_1(E,A,B)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(D))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(D))
=> ~ ( H = F
& I = G
& r1_subset_1(u1_struct_0(D),u1_struct_0(E))
& r4_fsm_1(A,B,D,E)
& C = k13_fsm_1(A,B,D,E)
& ~ r5_fsm_1(A,B,D,H,I)
& r5_fsm_1(A,B,C,F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t77_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v5_fsm_1(D,A,B)
& v7_fsm_1(D,A,B)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v5_fsm_1(E,A,B)
& v7_fsm_1(E,A,B)
& l2_fsm_1(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(D))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(D))
=> ~ ( H = F
& I = G
& r1_subset_1(u1_struct_0(E),u1_struct_0(D))
& r4_fsm_1(A,B,E,D)
& C = k13_fsm_1(A,B,E,D)
& ~ r5_fsm_1(A,B,D,H,I)
& r5_fsm_1(A,B,C,F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t78_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& v5_fsm_1(D,A,B)
& v7_fsm_1(D,A,B)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v6_group_1(E)
& v5_fsm_1(E,A,B)
& v7_fsm_1(E,A,B)
& l2_fsm_1(E,A,B) )
=> ( ( r1_subset_1(u1_struct_0(D),u1_struct_0(E))
& r4_fsm_1(A,B,D,E)
& C = k13_fsm_1(A,B,D,E) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C)))
=> ! [G] :
( m1_subset_1(G,F)
=> ! [H] :
( m1_subset_1(H,F)
=> ~ ( r2_hidden(G,u1_struct_0(D))
& r2_hidden(H,u1_struct_0(D))
& G != H ) ) ) ) ) ) ) ) ) ) ).
fof(t79_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& v5_fsm_1(D,A,B)
& v7_fsm_1(D,A,B)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v6_group_1(E)
& v5_fsm_1(E,A,B)
& v7_fsm_1(E,A,B)
& l2_fsm_1(E,A,B) )
=> ( ( r1_subset_1(u1_struct_0(D),u1_struct_0(E))
& r4_fsm_1(A,B,D,E)
& C = k13_fsm_1(A,B,D,E) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C)))
=> ! [G] :
( m1_subset_1(G,F)
=> ! [H] :
( m1_subset_1(H,F)
=> ~ ( r2_hidden(G,u1_struct_0(E))
& r2_hidden(H,u1_struct_0(E))
& G != H ) ) ) ) ) ) ) ) ) ) ).
fof(t80_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& v5_fsm_1(D,A,B)
& v7_fsm_1(D,A,B)
& l2_fsm_1(D,A,B) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v6_group_1(E)
& v5_fsm_1(E,A,B)
& v7_fsm_1(E,A,B)
& l2_fsm_1(E,A,B) )
=> ( ( r1_subset_1(u1_struct_0(D),u1_struct_0(E))
& r4_fsm_1(A,B,D,E)
& C = k13_fsm_1(A,B,D,E) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C)))
=> ? [G] :
( m1_subset_1(G,F)
& ? [H] :
( m1_subset_1(H,F)
& r2_hidden(G,u1_struct_0(D))
& r2_hidden(H,u1_struct_0(E))
& ! [I] :
( m1_subset_1(I,F)
=> ( I = G
| I = H ) ) ) ) ) ) ) ) ) ) ) ).
fof(t81_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& l2_fsm_1(D,A,B) )
=> ? [E] :
( ~ v3_struct_0(E)
& v6_group_1(E)
& l2_fsm_1(E,A,B)
& ? [F] :
( ~ v3_struct_0(F)
& v6_group_1(F)
& l2_fsm_1(F,A,B)
& r1_subset_1(u1_struct_0(E),u1_struct_0(F))
& r7_fsm_1(A,B,E,C)
& r7_fsm_1(A,B,F,D) ) ) ) ) ) ) ).
fof(t82_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ( r7_fsm_1(A,B,C,D)
=> r4_fsm_1(A,B,C,D) ) ) ) ) ) ).
fof(t83_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& v5_fsm_1(C,A,B)
& v7_fsm_1(C,A,B)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& v5_fsm_1(D,A,B)
& v7_fsm_1(D,A,B)
& l2_fsm_1(D,A,B) )
=> ( ( r1_subset_1(u1_struct_0(C),u1_struct_0(D))
& r4_fsm_1(A,B,C,D) )
=> r7_fsm_1(A,B,C,D) ) ) ) ) ) ).
fof(t84_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& v7_fsm_1(C,A,B)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& v7_fsm_1(D,A,B)
& l2_fsm_1(D,A,B) )
=> ( r4_fsm_1(A,B,C,D)
=> r7_fsm_1(A,B,k11_fsm_1(A,B,C),k11_fsm_1(A,B,D)) ) ) ) ) ) ).
fof(t85_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_group_1(C)
& v5_fsm_1(C,A,B)
& v7_fsm_1(C,A,B)
& l2_fsm_1(C,A,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v6_group_1(D)
& v5_fsm_1(D,A,B)
& v7_fsm_1(D,A,B)
& l2_fsm_1(D,A,B) )
=> ( r7_fsm_1(A,B,C,D)
<=> r4_fsm_1(A,B,C,D) ) ) ) ) ) ).
fof(dt_l1_fsm_1,axiom,
! [A,B] :
( l1_fsm_1(B,A)
=> l1_struct_0(B) ) ).
fof(existence_l1_fsm_1,axiom,
! [A] :
? [B] : l1_fsm_1(B,A) ).
fof(dt_l2_fsm_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( l2_fsm_1(C,A,B)
=> l1_fsm_1(C,A) ) ) ).
fof(existence_l2_fsm_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ? [C] : l2_fsm_1(C,A,B) ) ).
fof(dt_l3_fsm_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( l3_fsm_1(C,A,B)
=> l1_fsm_1(C,A) ) ) ).
fof(existence_l3_fsm_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ? [C] : l3_fsm_1(C,A,B) ) ).
fof(abstractness_v1_fsm_1,axiom,
! [A,B] :
( l1_fsm_1(B,A)
=> ( v1_fsm_1(B,A)
=> B = g1_fsm_1(A,u1_struct_0(B),u1_fsm_1(A,B),u2_fsm_1(A,B)) ) ) ).
fof(abstractness_v2_fsm_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& l2_fsm_1(C,A,B) )
=> ( v2_fsm_1(C,A,B)
=> C = g2_fsm_1(A,B,u1_struct_0(C),u1_fsm_1(B,C),u3_fsm_1(A,B,C),u2_fsm_1(B,C)) ) ) ).
fof(abstractness_v3_fsm_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& l3_fsm_1(C,A,B) )
=> ( v3_fsm_1(C,A,B)
=> C = g3_fsm_1(A,B,u1_struct_0(C),u1_fsm_1(B,C),u4_fsm_1(A,B,C),u2_fsm_1(B,C)) ) ) ).
fof(symmetry_r4_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l2_fsm_1(C,A,B)
& ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ( r4_fsm_1(A,B,C,D)
=> r4_fsm_1(A,B,D,C) ) ) ).
fof(reflexivity_r4_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l2_fsm_1(C,A,B)
& ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> r4_fsm_1(A,B,C,C) ) ).
fof(symmetry_r5_fsm_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l2_fsm_1(C,A,B)
& m1_subset_1(D,u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(C)) )
=> ( r5_fsm_1(A,B,C,D,E)
=> r5_fsm_1(A,B,C,E,D) ) ) ).
fof(reflexivity_r5_fsm_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l2_fsm_1(C,A,B)
& m1_subset_1(D,u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(C)) )
=> r5_fsm_1(A,B,C,D,D) ) ).
fof(symmetry_r7_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l2_fsm_1(C,A,B)
& ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ( r7_fsm_1(A,B,C,D)
=> r7_fsm_1(A,B,D,C) ) ) ).
fof(reflexivity_r7_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l2_fsm_1(C,A,B)
& ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> r7_fsm_1(A,B,C,C) ) ).
fof(dt_k1_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_fsm_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,u1_struct_0(B)) )
=> m1_subset_1(k1_fsm_1(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k2_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_fsm_1(B,A)
& m1_subset_1(C,u1_struct_0(B))
& m1_finseq_1(D,A) )
=> m2_finseq_1(k2_fsm_1(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k3_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_fsm_1(B,A)
& m1_subset_1(C,u1_struct_0(B))
& m1_finseq_1(D,A) )
=> m1_subset_1(k3_fsm_1(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k4_fsm_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l2_fsm_1(C,A,B)
& m1_subset_1(D,u1_struct_0(C))
& m1_finseq_1(E,A) )
=> m2_finseq_1(k4_fsm_1(A,B,C,D,E),B) ) ).
fof(dt_k5_fsm_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l3_fsm_1(C,A,B)
& m1_subset_1(D,u1_struct_0(C))
& m1_finseq_1(E,A) )
=> m2_finseq_1(k5_fsm_1(A,B,C,D,E),B) ) ).
fof(dt_k6_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l2_fsm_1(C,A,B)
& m1_subset_1(D,k5_numbers) )
=> ( v3_relat_2(k6_fsm_1(A,B,C,D))
& v8_relat_2(k6_fsm_1(A,B,C,D))
& v1_partfun1(k6_fsm_1(A,B,C,D),u1_struct_0(C),u1_struct_0(C))
& m2_relset_1(k6_fsm_1(A,B,C,D),u1_struct_0(C),u1_struct_0(C)) ) ) ).
fof(dt_k7_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l2_fsm_1(C,A,B)
& m1_subset_1(D,k5_numbers) )
=> ( ~ v1_xboole_0(k7_fsm_1(A,B,C,D))
& m1_eqrel_1(k7_fsm_1(A,B,C,D),u1_struct_0(C)) ) ) ).
fof(dt_k8_fsm_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> m1_eqrel_1(k8_fsm_1(A,B,C),u1_struct_0(C)) ) ).
fof(dt_k9_fsm_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B)
& m1_subset_1(D,k8_fsm_1(A,B,C))
& m1_subset_1(E,A) )
=> m2_subset_1(k9_fsm_1(A,B,C,D,E),k1_zfmisc_1(u1_struct_0(C)),k8_fsm_1(A,B,C)) ) ).
fof(dt_k10_fsm_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B)
& m1_subset_1(D,k8_fsm_1(A,B,C))
& m1_subset_1(E,A) )
=> m1_subset_1(k10_fsm_1(A,B,C,D,E),B) ) ).
fof(dt_k11_fsm_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& v6_group_1(C)
& l2_fsm_1(C,A,B) )
=> ( v2_fsm_1(k11_fsm_1(A,B,C),A,B)
& l2_fsm_1(k11_fsm_1(A,B,C),A,B) ) ) ).
fof(dt_k12_fsm_1,axiom,
$true ).
fof(dt_k13_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& l2_fsm_1(C,A,B)
& ~ v3_struct_0(D)
& l2_fsm_1(D,A,B) )
=> ( v2_fsm_1(k13_fsm_1(A,B,C,D),A,B)
& l2_fsm_1(k13_fsm_1(A,B,C,D),A,B) ) ) ).
fof(dt_u1_fsm_1,axiom,
! [A,B] :
( l1_fsm_1(B,A)
=> ( v1_funct_1(u1_fsm_1(A,B))
& v1_funct_2(u1_fsm_1(A,B),k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B))
& m2_relset_1(u1_fsm_1(A,B),k2_zfmisc_1(u1_struct_0(B),A),u1_struct_0(B)) ) ) ).
fof(dt_u2_fsm_1,axiom,
! [A,B] :
( l1_fsm_1(B,A)
=> m1_subset_1(u2_fsm_1(A,B),u1_struct_0(B)) ) ).
fof(dt_u3_fsm_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& l2_fsm_1(C,A,B) )
=> ( v1_funct_1(u3_fsm_1(A,B,C))
& v1_funct_2(u3_fsm_1(A,B,C),k2_zfmisc_1(u1_struct_0(C),A),B)
& m2_relset_1(u3_fsm_1(A,B,C),k2_zfmisc_1(u1_struct_0(C),A),B) ) ) ).
fof(dt_u4_fsm_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& l3_fsm_1(C,A,B) )
=> ( v1_funct_1(u4_fsm_1(A,B,C))
& v1_funct_2(u4_fsm_1(A,B,C),u1_struct_0(C),B)
& m2_relset_1(u4_fsm_1(A,B,C),u1_struct_0(C),B) ) ) ).
fof(dt_g1_fsm_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,A),B)
& m1_relset_1(C,k2_zfmisc_1(B,A),B)
& m1_subset_1(D,B) )
=> ( v1_fsm_1(g1_fsm_1(A,B,C,D),A)
& l1_fsm_1(g1_fsm_1(A,B,C,D),A) ) ) ).
fof(free_g1_fsm_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,A),B)
& m1_relset_1(C,k2_zfmisc_1(B,A),B)
& m1_subset_1(D,B) )
=> ! [E,F,G,H] :
( g1_fsm_1(A,B,C,D) = g1_fsm_1(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
fof(dt_g2_fsm_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,A),C)
& m1_relset_1(D,k2_zfmisc_1(C,A),C)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(C,A),B)
& m1_relset_1(E,k2_zfmisc_1(C,A),B)
& m1_subset_1(F,C) )
=> ( v2_fsm_1(g2_fsm_1(A,B,C,D,E,F),A,B)
& l2_fsm_1(g2_fsm_1(A,B,C,D,E,F),A,B) ) ) ).
fof(free_g2_fsm_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,A),C)
& m1_relset_1(D,k2_zfmisc_1(C,A),C)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(C,A),B)
& m1_relset_1(E,k2_zfmisc_1(C,A),B)
& m1_subset_1(F,C) )
=> ! [G,H,I,J,K,L] :
( g2_fsm_1(A,B,C,D,E,F) = g2_fsm_1(G,H,I,J,K,L)
=> ( A = G
& B = H
& C = I
& D = J
& E = K
& F = L ) ) ) ).
fof(dt_g3_fsm_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,A),C)
& m1_relset_1(D,k2_zfmisc_1(C,A),C)
& v1_funct_1(E)
& v1_funct_2(E,C,B)
& m1_relset_1(E,C,B)
& m1_subset_1(F,C) )
=> ( v3_fsm_1(g3_fsm_1(A,B,C,D,E,F),A,B)
& l3_fsm_1(g3_fsm_1(A,B,C,D,E,F),A,B) ) ) ).
fof(free_g3_fsm_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(C,A),C)
& m1_relset_1(D,k2_zfmisc_1(C,A),C)
& v1_funct_1(E)
& v1_funct_2(E,C,B)
& m1_relset_1(E,C,B)
& m1_subset_1(F,C) )
=> ! [G,H,I,J,K,L] :
( g3_fsm_1(A,B,C,D,E,F) = g3_fsm_1(G,H,I,J,K,L)
=> ( A = G
& B = H
& C = I
& D = J
& E = K
& F = L ) ) ) ).
fof(d23_fsm_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_1(C,A,B) )
=> k12_fsm_1(A,B,C) = a_3_0_fsm_1(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_fsm_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& ~ v3_struct_0(D)
& l2_fsm_1(D,B,C) )
=> ( r2_hidden(A,a_3_0_fsm_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(D))
& A = E
& v6_fsm_1(E,B,C,D) ) ) ) ).
%------------------------------------------------------------------------------