SET007 Axioms: SET007+711.ax
%------------------------------------------------------------------------------
% File : SET007+711 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On State Machines of Calculating Type
% 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 62 ( 1 unt; 0 def)
% Number of atoms : 602 ( 118 equ)
% Maximal formula atoms : 28 ( 9 avg)
% Number of connectives : 697 ( 157 ~; 3 |; 252 &)
% ( 9 <=>; 276 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 12 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 0 prp; 1-5 aty)
% Number of functors : 39 ( 39 usr; 5 con; 0-7 aty)
% Number of variables : 307 ( 294 !; 13 ?)
% 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_fsm_2,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) )
=> ( ~ v1_xboole_0(k2_fsm_1(A,B,C,D))
& v1_relat_1(k2_fsm_1(A,B,C,D))
& v1_funct_1(k2_fsm_1(A,B,C,D))
& v1_finset_1(k2_fsm_1(A,B,C,D))
& v1_finseq_1(k2_fsm_1(A,B,C,D)) ) ) ).
fof(rc1_fsm_2,axiom,
! [A] :
? [B] :
( l1_fsm_2(B,A)
& v4_fsm_2(B,A) ) ).
fof(rc2_fsm_2,axiom,
! [A] :
? [B] :
( l1_fsm_2(B,A)
& ~ v3_struct_0(B) ) ).
fof(rc3_fsm_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ? [C] :
( l2_fsm_2(C,A,B)
& v6_fsm_2(C,A,B) ) ) ).
fof(rc4_fsm_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ? [C] :
( l2_fsm_2(C,A,B)
& ~ v3_struct_0(C)
& v6_fsm_2(C,A,B) ) ) ).
fof(fc2_fsm_2,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(E)
& v1_funct_2(E,k2_tarski(C,D),B)
& m1_relset_1(E,k2_tarski(C,D),B) )
=> ( ~ v3_struct_0(k1_fsm_2(A,B,C,D,E))
& v1_fsm_2(k1_fsm_2(A,B,C,D,E),A)
& v6_fsm_2(k1_fsm_2(A,B,C,D,E),A,B) ) ) ).
fof(fc3_fsm_2,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(E)
& v1_funct_2(E,k2_tarski(C,D),B)
& m1_relset_1(E,k2_tarski(C,D),B) )
=> ( ~ v3_struct_0(k1_fsm_2(A,B,C,D,E))
& v1_fsm_2(k1_fsm_2(A,B,C,D,E),A)
& v5_fsm_2(k1_fsm_2(A,B,C,D,E),A)
& v6_fsm_2(k1_fsm_2(A,B,C,D,E),A,B) ) ) ).
fof(rc5_fsm_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ? [C] :
( l2_fsm_2(C,A,B)
& ~ v3_struct_0(C)
& v1_fsm_2(C,A)
& v5_fsm_2(C,A) ) ) ).
fof(rc6_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( l1_fsm_2(B,A)
& ~ v3_struct_0(B)
& v1_fsm_2(B,A)
& v5_fsm_2(B,A) ) ) ).
fof(t1_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_fsm_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> k2_fsm_1(A,C,D,k12_finseq_1(A,B)) = k2_finseq_4(u1_struct_0(C),D,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,D,B))) ) ) ) ) ).
fof(t2_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_fsm_1(D,A) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> k2_fsm_1(A,D,E,k2_finseq_4(A,B,C)) = k3_finseq_4(u1_struct_0(D),E,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,E,B)),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(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,E,B)),C))) ) ) ) ) ) ).
fof(t3_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( ( ~ v3_struct_0(E)
& l1_fsm_1(E,A) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(E))
=> k2_fsm_1(A,E,F,k3_finseq_4(A,B,C,D)) = k3_scmpds_1(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,F,B)),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,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,F,B)),C)),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,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,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,F,B)),C)),D))) ) ) ) ) ) ) ).
fof(d1_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ( v1_fsm_2(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( m2_finseq_1(E,A)
=> ( ( k1_funct_1(D,np__1) = k1_funct_1(E,np__1)
& r1_xreal_0(C,k1_nat_1(k3_finseq_1(D),np__1))
& r1_xreal_0(C,k1_nat_1(k3_finseq_1(E),np__1)) )
=> k1_funct_1(k2_fsm_1(A,B,u2_fsm_1(A,B),D),C) = k1_funct_1(k2_fsm_1(A,B,u2_fsm_1(A,B),E),C) ) ) ) ) ) ) ) ).
fof(t4_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ( v1_fsm_2(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ( k1_funct_1(C,np__1) = k1_funct_1(D,np__1)
=> r3_xboole_0(k2_fsm_1(A,B,u2_fsm_1(A,B),C),k2_fsm_1(A,B,u2_fsm_1(A,B),D)) ) ) ) ) ) ) ).
fof(t5_fsm_2,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)
=> ( k1_funct_1(C,np__1) = k1_funct_1(D,np__1)
=> r3_xboole_0(k2_fsm_1(A,B,u2_fsm_1(A,B),C),k2_fsm_1(A,B,u2_fsm_1(A,B),D)) ) ) )
=> v1_fsm_2(B,A) ) ) ) ).
fof(t6_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ( v1_fsm_2(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ( ( k1_funct_1(C,np__1) = k1_funct_1(D,np__1)
& k3_finseq_1(C) = k3_finseq_1(D) )
=> k2_fsm_1(A,B,u2_fsm_1(A,B),C) = k2_fsm_1(A,B,u2_fsm_1(A,B),D) ) ) ) ) ) ) ).
fof(t7_fsm_2,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)
=> ( ( k1_funct_1(C,np__1) = k1_funct_1(D,np__1)
& k3_finseq_1(C) = k3_finseq_1(D) )
=> k2_fsm_1(A,B,u2_fsm_1(A,B),C) = k2_fsm_1(A,B,u2_fsm_1(A,B),D) ) ) )
=> v1_fsm_2(B,A) ) ) ) ).
fof(d2_fsm_2,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] :
( m1_subset_1(D,A)
=> ( r1_fsm_2(A,B,C,D)
<=> ? [E] :
( m2_finseq_1(E,A)
& r1_fsm_1(A,B,k8_finseq_1(A,k12_finseq_1(A,D),E),u2_fsm_1(A,B),C) ) ) ) ) ) ) ).
fof(d3_fsm_2,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))
=> ( v2_fsm_2(C,A,B)
<=> ? [D] :
( m2_finseq_1(D,A)
& r1_fsm_1(A,B,D,u2_fsm_1(A,B),C) ) ) ) ) ) ).
fof(t8_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_fsm_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( r1_fsm_2(A,C,D,B)
=> v2_fsm_2(D,A,C) ) ) ) ) ) ).
fof(t9_fsm_2,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))
=> ~ ( v2_fsm_2(C,A,B)
& C != u2_fsm_1(A,B)
& ! [D] :
( m1_subset_1(D,A)
=> ~ r1_fsm_2(A,B,C,D) ) ) ) ) ) ).
fof(t10_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> v2_fsm_2(u2_fsm_1(A,B),A,B) ) ) ).
fof(t11_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_fsm_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ~ ( v1_fsm_2(C,A)
& r1_fsm_2(A,C,D,B)
& ! [E] :
( ( ~ v1_xboole_0(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ? [F] :
( m2_finseq_1(F,A)
& r1_xreal_0(E,k1_nat_1(k3_finseq_1(F),np__1))
& k1_funct_1(F,np__1) = B
& ~ ( D = k1_funct_1(k2_fsm_1(A,C,u2_fsm_1(A,C),F),E)
& ! [G] :
( ( ~ v1_xboole_0(G)
& m2_subset_1(G,k1_numbers,k5_numbers) )
=> ~ ( ~ r1_xreal_0(E,G)
& k1_funct_1(k2_fsm_1(A,C,u2_fsm_1(A,C),F),G) = D ) ) ) ) ) ) ) ) ) ) ).
fof(d4_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ( v3_fsm_2(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> v2_fsm_2(C,A,B) ) ) ) ) ).
fof(t12_fsm_2,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,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> 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,E,C)) = 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,E,D)) ) ) )
=> v1_fsm_2(B,A) ) ) ) ).
fof(t13_fsm_2,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,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( E != u2_fsm_1(A,B)
=> 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,E,C)) = 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,E,D)) ) ) ) )
& ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> 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)) != u2_fsm_1(A,B) ) ) )
=> v1_fsm_2(B,A) ) ) ) ).
fof(t14_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ( ( v3_fsm_2(B,A)
& v1_fsm_2(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( E != u2_fsm_1(A,B)
=> k1_funct_1(k2_fsm_1(A,B,E,k12_finseq_1(A,C)),np__2) = k1_funct_1(k2_fsm_1(A,B,E,k12_finseq_1(A,D)),np__2) ) ) ) ) ) ) ) ).
fof(t15_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ( ( v3_fsm_2(B,A)
& v1_fsm_2(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( E != u2_fsm_1(A,B)
=> 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,E,C)) = 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,E,D)) ) ) ) ) ) ) ) ).
fof(t16_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_1(B,A) )
=> ( ( v3_fsm_2(B,A)
& v1_fsm_2(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ~ ( 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,u2_fsm_1(A,B),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,u2_fsm_1(A,B),E))
& 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,F,C)) = u2_fsm_1(A,B) ) ) ) ) ) ) ) ) ).
fof(d5_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_fsm_2(C,A) )
=> ( r2_fsm_2(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& r1_fsm_2(A,C,D,B)
& r2_hidden(D,u1_fsm_2(A,C)) ) ) ) ) ) ).
fof(d6_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_fsm_2(B,A) )
=> ( v5_fsm_2(B,A)
<=> ! [C] :
( m1_subset_1(C,A)
=> r2_fsm_2(A,C,B) ) ) ) ) ).
fof(d7_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C,D,E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_tarski(C,D),B)
& m2_relset_1(E,k2_tarski(C,D),B) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& v6_fsm_2(F,A,B)
& l2_fsm_2(F,A,B) )
=> ( F = k1_fsm_2(A,B,C,D,E)
<=> ( u1_struct_0(F) = k2_tarski(C,D)
& u1_fsm_1(A,F) = k2_funcop_1(k2_zfmisc_1(k2_tarski(C,D),A),D)
& u4_fsm_1(A,B,F) = E
& u2_fsm_1(A,F) = C
& u1_fsm_2(A,F) = k1_tarski(D) ) ) ) ) ) ) ).
fof(t17_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,B)
=> ! [D,E,F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_tarski(D,E),A)
& m2_relset_1(F,k2_tarski(D,E),A) )
=> ! [G] :
( ( ~ v1_xboole_0(G)
& m2_subset_1(G,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(G,k1_nat_1(k3_finseq_1(C),np__1))
=> ( r1_xreal_0(G,np__1)
| k1_funct_1(k2_fsm_1(B,k1_fsm_2(B,A,D,E,F),u2_fsm_1(B,k1_fsm_2(B,A,D,E,F)),C),G) = E ) ) ) ) ) ) ) ).
fof(t18_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_2(D,B,A) )
=> ~ ( v1_fsm_2(D,B)
& r2_fsm_2(B,C,D)
& ~ r2_hidden(u2_fsm_1(B,D),u1_fsm_2(B,D))
& ! [E] :
( ( ~ v1_xboole_0(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ~ ( ! [F] :
( m2_finseq_1(F,B)
=> ( ( r1_xreal_0(E,k1_nat_1(k3_finseq_1(F),np__1))
& k1_funct_1(F,np__1) = C )
=> r2_hidden(k1_funct_1(k2_fsm_1(B,D,u2_fsm_1(B,D),F),E),u1_fsm_2(B,D)) ) )
& ! [F] :
( m2_finseq_1(F,B)
=> ! [G] :
( ( ~ v1_xboole_0(G)
& m2_subset_1(G,k1_numbers,k5_numbers) )
=> ~ ( r1_xreal_0(G,k1_nat_1(k3_finseq_1(F),np__1))
& k1_funct_1(F,np__1) = C
& ~ r1_xreal_0(E,G)
& r2_hidden(k1_funct_1(k2_fsm_1(B,D,u2_fsm_1(B,D),F),G),u1_fsm_2(B,D)) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_2(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( r3_fsm_2(A,B,C,D,E)
<=> ? [F] :
( ~ v1_xboole_0(F)
& m2_subset_1(F,k1_numbers,k5_numbers)
& ! [G] :
( m2_finseq_1(G,A)
=> ( k1_funct_1(G,np__1) = D
=> ( ( r1_xreal_0(F,k1_nat_1(k3_finseq_1(G),np__1))
=> ( E = k1_funct_1(u4_fsm_1(A,B,C),k1_funct_1(k2_fsm_1(A,C,u2_fsm_1(A,C),G),F))
& r2_hidden(k1_funct_1(k2_fsm_1(A,C,u2_fsm_1(A,C),G),F),u1_fsm_2(A,C)) ) )
& ! [H] :
( ( ~ v1_xboole_0(H)
& m2_subset_1(H,k1_numbers,k5_numbers) )
=> ~ ( ~ r1_xreal_0(F,H)
& r1_xreal_0(H,k1_nat_1(k3_finseq_1(G),np__1))
& r2_hidden(k1_funct_1(k2_fsm_1(A,C,u2_fsm_1(A,C),G),H),u1_fsm_2(A,C)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_2(D,A,B) )
=> ( r2_hidden(u2_fsm_1(A,D),u1_fsm_2(A,D))
=> r3_fsm_2(A,B,D,C,k8_funct_2(u1_struct_0(D),B,u4_fsm_1(A,B,D),u2_fsm_1(A,D))) ) ) ) ) ) ).
fof(t20_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_2(D,A,B) )
=> ~ ( v1_fsm_2(D,A)
& r2_fsm_2(A,C,D)
& ~ r2_hidden(u2_fsm_1(A,D),u1_fsm_2(A,D))
& ! [E] :
( m1_subset_1(E,B)
=> ~ r3_fsm_2(A,B,D,C,E) ) ) ) ) ) ) ).
fof(t21_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_fsm_2(D,A,B) )
=> ( ( v1_fsm_2(D,A)
& r2_fsm_2(A,C,D) )
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( m1_subset_1(F,B)
=> ( ( r3_fsm_2(A,B,D,C,E)
& r3_fsm_2(A,B,D,C,F) )
=> E = F ) ) ) ) ) ) ) ) ).
fof(t22_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_fsm_2(C,k2_zfmisc_1(A,A),k2_xboole_0(A,k1_tarski(A))) )
=> ( ( v1_fsm_2(C,k2_zfmisc_1(A,A))
& u1_struct_0(C) = k2_xboole_0(A,k1_tarski(A))
& u1_fsm_2(k2_zfmisc_1(A,A),C) = A
& u2_fsm_1(k2_zfmisc_1(A,A),C) = A
& u4_fsm_1(k2_zfmisc_1(A,A),k2_xboole_0(A,k1_tarski(A)),C) = k6_partfun1(u1_struct_0(C))
& ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(C),k2_zfmisc_1(A,A)),u1_struct_0(C),u1_fsm_1(k2_zfmisc_1(A,A),C),k1_domain_1(u1_struct_0(C),k2_zfmisc_1(A,A),u2_fsm_1(k2_zfmisc_1(A,A),C),k1_domain_1(A,A,D,E))) = k2_binop_1(A,A,A,B,D,E) ) ) )
=> ( v5_fsm_2(C,k2_zfmisc_1(A,A))
& ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> r3_fsm_2(k2_zfmisc_1(A,A),k2_xboole_0(A,k1_tarski(A)),C,k1_domain_1(A,A,D,E),k2_binop_1(A,A,A,B,D,E)) ) ) ) ) ) ) ) ).
fof(t23_fsm_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
=> ( ( v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
& u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_xreal_0(C,B)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = B ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ~ r1_xreal_0(C,B)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = C ) ) ) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> r3_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C),k4_square_1(B,C)) ) ) ) ) ).
fof(t24_fsm_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
=> ( ( v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
& u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ~ r1_xreal_0(C,B)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = B ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_xreal_0(C,B)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = C ) ) ) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> r3_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C),k3_square_1(B,C)) ) ) ) ) ).
fof(t25_fsm_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
=> ( ( v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
& u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = k3_real_1(B,C) ) ) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> r3_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C),k3_real_1(B,C)) ) ) ) ) ).
fof(t26_fsm_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
=> ( ( v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
& u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ~ ( r1_xreal_0(B,np__0)
& r1_xreal_0(C,np__0) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = np__1 ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ( r1_xreal_0(B,np__0)
& r1_xreal_0(C,np__0) )
=> ( ( B != np__0
& C != np__0 )
| k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = np__0 ) ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(np__0,B)
& ~ r1_xreal_0(np__0,C)
& k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) != k1_real_1(np__1) ) ) ) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> r3_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C),k4_square_1(k2_absvalue(B),k2_absvalue(C))) ) ) ) ) ).
fof(d9_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_fsm_2(C,A)
& v5_fsm_2(C,A)
& l2_fsm_2(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,B)
=> ( E = k2_fsm_2(A,B,C,D)
<=> r3_fsm_2(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t27_fsm_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k7_domain_1(k1_numbers,np__0,np__1),A)
& m2_relset_1(D,k7_domain_1(k1_numbers,np__0,np__1),A) )
=> k2_fsm_2(B,A,k1_fsm_2(B,A,np__0,np__1,D),C) = k1_funct_1(D,np__1) ) ) ) ) ).
fof(t28_fsm_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& v5_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
=> ( ( u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
& u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_xreal_0(C,B)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = B ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ~ r1_xreal_0(C,B)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = C ) ) ) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k2_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C)) = k4_square_1(B,C) ) ) ) ) ).
fof(t29_fsm_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& v5_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
=> ( ( u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
& u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ~ r1_xreal_0(C,B)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = B ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_xreal_0(C,B)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = C ) ) ) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k2_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C)) = k3_square_1(B,C) ) ) ) ) ).
fof(t30_fsm_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& v5_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
=> ( ( u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
& u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = k3_real_1(B,C) ) ) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k2_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C)) = k3_real_1(B,C) ) ) ) ) ).
fof(t31_fsm_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& v5_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers))
& l2_fsm_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))) )
=> ( ( u1_struct_0(A) = k2_xboole_0(k1_numbers,k1_tarski(k1_numbers))
& u1_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A) = k1_numbers
& u4_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A) = k6_partfun1(u1_struct_0(A))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ~ ( r1_xreal_0(B,np__0)
& r1_xreal_0(C,np__0) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = np__1 ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ( r1_xreal_0(B,np__0)
& r1_xreal_0(C,np__0) )
=> ( ( B != np__0
& C != np__0 )
| k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) = np__0 ) ) ) )
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(np__0,B)
& ~ r1_xreal_0(np__0,C)
& k8_funct_2(k2_zfmisc_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers)),u1_struct_0(A),u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(u1_struct_0(A),k2_zfmisc_1(k1_numbers,k1_numbers),u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k1_domain_1(k1_numbers,k1_numbers,B,C))) != k1_real_1(np__1) ) ) ) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k2_fsm_2(k2_zfmisc_1(k1_numbers,k1_numbers),k2_xboole_0(k1_numbers,k1_tarski(k1_numbers)),A,k1_domain_1(k1_numbers,k1_numbers,B,C)) = k4_square_1(k2_absvalue(B),k2_absvalue(C)) ) ) ) ) ).
fof(dt_l1_fsm_2,axiom,
! [A,B] :
( l1_fsm_2(B,A)
=> l1_fsm_1(B,A) ) ).
fof(existence_l1_fsm_2,axiom,
! [A] :
? [B] : l1_fsm_2(B,A) ).
fof(dt_l2_fsm_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( l2_fsm_2(C,A,B)
=> ( l1_fsm_2(C,A)
& l3_fsm_1(C,A,B) ) ) ) ).
fof(existence_l2_fsm_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ? [C] : l2_fsm_2(C,A,B) ) ).
fof(abstractness_v4_fsm_2,axiom,
! [A,B] :
( l1_fsm_2(B,A)
=> ( v4_fsm_2(B,A)
=> B = g1_fsm_2(A,u1_struct_0(B),u1_fsm_1(A,B),u2_fsm_1(A,B),u1_fsm_2(A,B)) ) ) ).
fof(abstractness_v6_fsm_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& l2_fsm_2(C,A,B) )
=> ( v6_fsm_2(C,A,B)
=> C = g2_fsm_2(A,B,u1_struct_0(C),u1_fsm_1(B,C),u4_fsm_1(A,B,C),u2_fsm_1(B,C),u1_fsm_2(B,C)) ) ) ).
fof(dt_k1_fsm_2,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(E)
& v1_funct_2(E,k2_tarski(C,D),B)
& m1_relset_1(E,k2_tarski(C,D),B) )
=> ( ~ v3_struct_0(k1_fsm_2(A,B,C,D,E))
& v6_fsm_2(k1_fsm_2(A,B,C,D,E),A,B)
& l2_fsm_2(k1_fsm_2(A,B,C,D,E),A,B) ) ) ).
fof(dt_k2_fsm_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& v1_fsm_2(C,A)
& v5_fsm_2(C,A)
& l2_fsm_2(C,A,B)
& m1_subset_1(D,A) )
=> m1_subset_1(k2_fsm_2(A,B,C,D),B) ) ).
fof(dt_u1_fsm_2,axiom,
! [A,B] :
( l1_fsm_2(B,A)
=> m1_subset_1(u1_fsm_2(A,B),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_g1_fsm_2,axiom,
! [A,B,C,D,E] :
( ( 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)
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ( v4_fsm_2(g1_fsm_2(A,B,C,D,E),A)
& l1_fsm_2(g1_fsm_2(A,B,C,D,E),A) ) ) ).
fof(free_g1_fsm_2,axiom,
! [A,B,C,D,E] :
( ( 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)
& m1_subset_1(E,k1_zfmisc_1(B)) )
=> ! [F,G,H,I,J] :
( g1_fsm_2(A,B,C,D,E) = g1_fsm_2(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(dt_g2_fsm_2,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ 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)
& m1_subset_1(G,k1_zfmisc_1(C)) )
=> ( v6_fsm_2(g2_fsm_2(A,B,C,D,E,F,G),A,B)
& l2_fsm_2(g2_fsm_2(A,B,C,D,E,F,G),A,B) ) ) ).
fof(free_g2_fsm_2,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ 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)
& m1_subset_1(G,k1_zfmisc_1(C)) )
=> ! [H,I,J,K,L,M,N] :
( g2_fsm_2(A,B,C,D,E,F,G) = g2_fsm_2(H,I,J,K,L,M,N)
=> ( A = H
& B = I
& C = J
& D = K
& E = L
& F = M
& G = N ) ) ) ).
%------------------------------------------------------------------------------