SET007 Axioms: SET007+70.ax
%------------------------------------------------------------------------------
% File : SET007+70 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Binary Operations Applied to Finite Sequences
% 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 : finseqop [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 112 ( 6 unt; 0 def)
% Number of atoms : 1194 ( 132 equ)
% Maximal formula atoms : 22 ( 10 avg)
% Number of connectives : 1252 ( 170 ~; 2 |; 506 &)
% ( 3 <=>; 571 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 13 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 3 con; 0-6 aty)
% Number of variables : 571 ( 570 !; 1 ?)
% 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(t1_finseqop,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( k13_funct_3(k1_xboole_0,A) = k1_xboole_0
& k13_funct_3(A,k1_xboole_0) = k1_xboole_0 ) ) ).
fof(t2_finseqop,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( k15_funct_3(k1_xboole_0,A) = k1_xboole_0
& k15_funct_3(A,k1_xboole_0) = k1_xboole_0 ) ) ).
fof(t3_finseqop,axiom,
$true ).
fof(t4_finseqop,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( k3_funcop_1(A,k1_xboole_0,B) = k1_xboole_0
& k3_funcop_1(A,B,k1_xboole_0) = k1_xboole_0 ) ) ) ).
fof(t5_finseqop,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> k4_funcop_1(B,k1_xboole_0,A) = k1_xboole_0 ) ).
fof(t6_finseqop,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> k5_funcop_1(B,A,k1_xboole_0) = k1_xboole_0 ) ).
fof(t7_finseqop,axiom,
! [A,B,C] : k13_funct_3(k2_funcop_1(A,B),k2_funcop_1(A,C)) = k2_funcop_1(A,k4_tarski(B,C)) ).
fof(t8_finseqop,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D] :
( r2_hidden(k4_tarski(C,D),k1_relat_1(A))
=> k3_funcop_1(A,k2_funcop_1(B,C),k2_funcop_1(B,D)) = k2_funcop_1(B,k1_funct_1(A,k4_tarski(C,D))) ) ) ).
fof(t9_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> k5_finseqop(A,B,k8_finseq_1(A,D,k12_finseq_1(A,C)),E) = k8_finseq_1(B,k5_finseqop(A,B,D,E),k12_finseq_1(B,k8_funct_2(A,B,E,C))) ) ) ) ) ) ).
fof(t10_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> k5_finseqop(A,B,k8_finseq_1(A,C,D),E) = k8_finseq_1(B,k5_finseqop(A,B,C,E),k5_finseqop(A,B,D,E)) ) ) ) ) ) ).
fof(t11_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( m1_subset_1(E,C)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(B,C),A)
& m2_relset_1(G,k2_zfmisc_1(B,C),A) )
=> ! [H] :
( m2_finseq_2(H,B,k4_finseq_2(F,B))
=> ! [I] :
( m2_finseq_2(I,C,k4_finseq_2(F,C))
=> k1_finseqop(B,C,A,G,k8_finseq_1(B,H,k12_finseq_1(B,D)),k8_finseq_1(C,I,k12_finseq_1(C,E))) = k8_finseq_1(A,k1_finseqop(B,C,A,G,H,I),k12_finseq_1(A,k2_binop_1(B,C,A,G,D,E))) ) ) ) ) ) ) ) ) ) ).
fof(t12_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,C),A)
& m2_relset_1(F,k2_zfmisc_1(B,C),A) )
=> ! [G] :
( m2_finseq_2(G,B,k4_finseq_2(D,B))
=> ! [H] :
( m2_finseq_2(H,C,k4_finseq_2(D,C))
=> ! [I] :
( m2_finseq_2(I,B,k4_finseq_2(E,B))
=> ! [J] :
( m2_finseq_2(J,C,k4_finseq_2(E,C))
=> k1_finseqop(B,C,A,F,k8_finseq_1(B,G,I),k8_finseq_1(C,H,J)) = k8_finseq_1(A,k1_finseqop(B,C,A,F,G,H),k1_finseqop(B,C,A,F,I,J)) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,C)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,C),B)
& m2_relset_1(F,k2_zfmisc_1(A,C),B) )
=> ! [G] :
( m2_finseq_1(G,C)
=> k3_finseqop(A,C,B,F,D,k8_finseq_1(C,G,k12_finseq_1(C,E))) = k8_finseq_1(B,k3_finseqop(A,C,B,F,D,G),k12_finseq_1(B,k2_binop_1(A,C,B,F,D,E))) ) ) ) ) ) ) ) ).
fof(t14_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,C),B)
& m2_relset_1(E,k2_zfmisc_1(A,C),B) )
=> ! [F] :
( m2_finseq_1(F,C)
=> ! [G] :
( m2_finseq_1(G,C)
=> k3_finseqop(A,C,B,E,D,k8_finseq_1(C,F,G)) = k8_finseq_1(B,k3_finseqop(A,C,B,E,D,F),k3_finseqop(A,C,B,E,D,G)) ) ) ) ) ) ) ) ).
fof(t15_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(C,A),B)
& m2_relset_1(F,k2_zfmisc_1(C,A),B) )
=> ! [G] :
( m2_finseq_1(G,C)
=> k2_finseqop(C,A,B,F,k8_finseq_1(C,G,k12_finseq_1(C,D)),E) = k8_finseq_1(B,k2_finseqop(C,A,B,F,G,E),k12_finseq_1(B,k2_binop_1(C,A,B,F,D,E))) ) ) ) ) ) ) ) ).
fof(t16_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(C,A),B)
& m2_relset_1(E,k2_zfmisc_1(C,A),B) )
=> ! [F] :
( m2_finseq_1(F,C)
=> ! [G] :
( m2_finseq_1(G,C)
=> k2_finseqop(C,A,B,E,k8_finseq_1(C,F,G),D) = k8_finseq_1(B,k2_finseqop(C,A,B,E,F,D),k2_finseqop(C,A,B,E,G,D)) ) ) ) ) ) ) ) ).
fof(t17_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> k5_finseqop(A,B,k4_finseqop(A,D,C),E) = k4_finseqop(B,D,k8_funct_2(A,B,E,C)) ) ) ) ) ) ).
fof(t18_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(A,B),C)
& m2_relset_1(G,k2_zfmisc_1(A,B),C) )
=> k1_finseqop(A,B,C,G,k4_finseqop(A,F,D),k4_finseqop(B,F,E)) = k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)) ) ) ) ) ) ) ) ).
fof(t19_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(A,B),C)
& m2_relset_1(G,k2_zfmisc_1(A,B),C) )
=> k3_finseqop(A,B,C,G,D,k4_finseqop(B,F,E)) = k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)) ) ) ) ) ) ) ) ).
fof(t20_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(A,B),C)
& m2_relset_1(G,k2_zfmisc_1(A,B),C) )
=> k2_finseqop(A,B,C,G,k4_finseqop(A,F,D),E) = k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)) ) ) ) ) ) ) ) ).
fof(t21_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,C),B)
& m2_relset_1(F,k2_zfmisc_1(A,C),B) )
=> ! [G] :
( m2_finseq_2(G,C,k4_finseq_2(E,C))
=> k1_finseqop(A,C,B,F,k4_finseqop(A,E,D),G) = k3_finseqop(A,C,B,F,D,G) ) ) ) ) ) ) ) ).
fof(t22_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(C,A),B)
& m2_relset_1(F,k2_zfmisc_1(C,A),B) )
=> ! [G] :
( m2_finseq_2(G,C,k4_finseq_2(E,C))
=> k3_funcop_1(F,G,k4_finseqop(C,E,D)) = k4_funcop_1(F,G,D) ) ) ) ) ) ) ) ).
fof(t23_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,C),B)
& m2_relset_1(F,k2_zfmisc_1(A,C),B) )
=> ! [G] :
( m2_finseq_2(G,C,k4_finseq_2(E,C))
=> k3_finseqop(A,C,B,F,D,G) = k5_relat_1(G,k5_funcop_1(F,D,k6_partfun1(C))) ) ) ) ) ) ) ) ).
fof(t24_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(C,A),B)
& m2_relset_1(F,k2_zfmisc_1(C,A),B) )
=> ! [G] :
( m2_finseq_2(G,C,k4_finseq_2(E,C))
=> k4_funcop_1(F,G,D) = k5_relat_1(G,k4_funcop_1(F,k6_partfun1(C),D)) ) ) ) ) ) ) ) ).
fof(t25_finseqop,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,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ( v2_binop_1(F,B)
=> k7_funct_2(A,B,B,k6_funcop_1(B,A,F,D,E),k8_funcop_1(B,B,F,C,k6_partfun1(B))) = k6_funcop_1(B,A,F,k7_funct_2(A,B,B,D,k8_funcop_1(B,B,F,C,k6_partfun1(B))),E) ) ) ) ) ) ) ) ).
fof(t26_finseqop,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,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ( v2_binop_1(F,B)
=> k7_funct_2(A,B,B,k6_funcop_1(B,A,F,D,E),k7_funcop_1(B,B,F,k6_partfun1(B),C)) = k6_funcop_1(B,A,F,D,k7_funct_2(A,B,B,E,k7_funcop_1(B,B,F,k6_partfun1(B),C))) ) ) ) ) ) ) ) ).
fof(t27_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(C,A))
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(C,A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ( v2_binop_1(F,A)
=> k5_finseqop(A,A,k1_finseqop(A,A,A,F,D,E),k8_funcop_1(A,A,F,B,k6_partfun1(A))) = k1_finseqop(A,A,A,F,k5_finseqop(A,A,D,k8_funcop_1(A,A,F,B,k6_partfun1(A))),E) ) ) ) ) ) ) ) ).
fof(t28_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(C,A))
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(C,A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ( v2_binop_1(F,A)
=> k5_finseqop(A,A,k1_finseqop(A,A,A,F,D,E),k7_funcop_1(A,A,F,k6_partfun1(A),B)) = k1_finseqop(A,A,A,F,D,k5_finseqop(A,A,E,k7_funcop_1(A,A,F,k6_partfun1(A),B))) ) ) ) ) ) ) ) ).
fof(t29_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,A,k4_finseq_2(B,A))
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(B,A))
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(B,A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ( v2_binop_1(F,A)
=> k1_finseqop(A,A,A,F,k1_finseqop(A,A,A,F,C,D),E) = k1_finseqop(A,A,A,F,C,k1_finseqop(A,A,A,F,D,E)) ) ) ) ) ) ) ) ).
fof(t30_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(D,A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ( v2_binop_1(F,A)
=> k2_finseqop(A,A,A,F,k3_finseqop(A,A,A,F,B,E),C) = k3_finseqop(A,A,A,F,B,k2_finseqop(A,A,A,F,E,C)) ) ) ) ) ) ) ) ).
fof(t31_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(C,A))
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(C,A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ( v2_binop_1(F,A)
=> k1_finseqop(A,A,A,F,k2_finseqop(A,A,A,F,D,B),E) = k1_finseqop(A,A,A,F,D,k3_finseqop(A,A,A,F,B,E)) ) ) ) ) ) ) ) ).
fof(t32_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(D,A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ( v2_binop_1(F,A)
=> k3_finseqop(A,A,A,F,k2_binop_1(A,A,A,F,B,C),E) = k3_finseqop(A,A,A,F,B,k3_finseqop(A,A,A,F,C,E)) ) ) ) ) ) ) ) ).
fof(t33_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(D,A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ( v2_binop_1(F,A)
=> k2_finseqop(A,A,A,F,E,k2_binop_1(A,A,A,F,B,C)) = k2_finseqop(A,A,A,F,k2_finseqop(A,A,A,F,E,B),C) ) ) ) ) ) ) ) ).
fof(t34_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,A,k4_finseq_2(B,A))
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(B,A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ( v1_binop_1(E,A)
=> k1_finseqop(A,A,A,E,C,D) = k1_finseqop(A,A,A,E,D,C) ) ) ) ) ) ) ).
fof(t35_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(C,A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ( v1_binop_1(E,A)
=> k3_finseqop(A,A,A,E,B,D) = k2_finseqop(A,A,A,E,D,B) ) ) ) ) ) ) ).
fof(t36_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(B,B),B)
& m2_relset_1(G,k2_zfmisc_1(B,B),B) )
=> ( r6_binop_1(B,F,G)
=> k8_funcop_1(B,A,F,k2_binop_1(B,B,B,G,C,D),E) = k6_funcop_1(B,A,G,k8_funcop_1(B,A,F,C,E),k8_funcop_1(B,A,F,D,E)) ) ) ) ) ) ) ) ) ).
fof(t37_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(B,B),B)
& m2_relset_1(G,k2_zfmisc_1(B,B),B) )
=> ( r6_binop_1(B,F,G)
=> k7_funcop_1(B,A,F,E,k2_binop_1(B,B,B,G,C,D)) = k6_funcop_1(B,A,G,k7_funcop_1(B,A,F,E,C),k7_funcop_1(B,A,F,E,D)) ) ) ) ) ) ) ) ) ).
fof(t38_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,C)
& m2_relset_1(D,A,C) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,C,B)
& m2_relset_1(F,C,B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(C,C),C)
& m2_relset_1(G,k2_zfmisc_1(C,C),C) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(B,B),B)
& m2_relset_1(H,k2_zfmisc_1(B,B),B) )
=> ( ! [I] :
( m1_subset_1(I,C)
=> ! [J] :
( m1_subset_1(J,C)
=> k8_funct_2(C,B,F,k2_binop_1(C,C,C,G,I,J)) = k2_binop_1(B,B,B,H,k8_funct_2(C,B,F,I),k8_funct_2(C,B,F,J)) ) )
=> k7_funct_2(A,C,B,k6_funcop_1(C,A,G,D,E),F) = k6_funcop_1(B,A,H,k7_funct_2(A,C,B,D,F),k7_funct_2(A,C,B,E,F)) ) ) ) ) ) ) ) ) ) ).
fof(t39_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,C,B)
& m2_relset_1(F,C,B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(C,C),C)
& m2_relset_1(G,k2_zfmisc_1(C,C),C) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(B,B),B)
& m2_relset_1(H,k2_zfmisc_1(B,B),B) )
=> ( ! [I] :
( m1_subset_1(I,C)
=> ! [J] :
( m1_subset_1(J,C)
=> k8_funct_2(C,B,F,k2_binop_1(C,C,C,G,I,J)) = k2_binop_1(B,B,B,H,k8_funct_2(C,B,F,I),k8_funct_2(C,B,F,J)) ) )
=> k7_funct_2(A,C,B,k8_funcop_1(C,A,G,D,E),F) = k8_funcop_1(B,A,H,k8_funct_2(C,B,F,D),k7_funct_2(A,C,B,E,F)) ) ) ) ) ) ) ) ) ) ).
fof(t40_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,C)
& m2_relset_1(E,A,C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,C,B)
& m2_relset_1(F,C,B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(C,C),C)
& m2_relset_1(G,k2_zfmisc_1(C,C),C) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(B,B),B)
& m2_relset_1(H,k2_zfmisc_1(B,B),B) )
=> ( ! [I] :
( m1_subset_1(I,C)
=> ! [J] :
( m1_subset_1(J,C)
=> k8_funct_2(C,B,F,k2_binop_1(C,C,C,G,I,J)) = k2_binop_1(B,B,B,H,k8_funct_2(C,B,F,I),k8_funct_2(C,B,F,J)) ) )
=> k7_funct_2(A,C,B,k7_funcop_1(C,A,G,E,D),F) = k7_funcop_1(B,A,H,k7_funct_2(A,C,B,E,F),k8_funct_2(C,B,F,D)) ) ) ) ) ) ) ) ) ) ).
fof(t41_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [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,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,B)
& m2_relset_1(F,B,B) )
=> ( r7_binop_1(B,F,E)
=> k7_funct_2(A,B,B,k6_funcop_1(B,A,E,C,D),F) = k6_funcop_1(B,A,E,k7_funct_2(A,B,B,C,F),k7_funct_2(A,B,B,D,F)) ) ) ) ) ) ) ) ).
fof(t42_finseqop,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,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,B)
& m2_relset_1(F,B,B) )
=> ( r7_binop_1(B,F,E)
=> k7_funct_2(A,B,B,k8_funcop_1(B,A,E,C,D),F) = k8_funcop_1(B,A,E,k8_funct_2(B,B,F,C),k7_funct_2(A,B,B,D,F)) ) ) ) ) ) ) ) ).
fof(t43_finseqop,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,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,B)
& m2_relset_1(F,B,B) )
=> ( r7_binop_1(B,F,E)
=> k7_funct_2(A,B,B,k7_funcop_1(B,A,E,D,C),F) = k7_funcop_1(B,A,E,k7_funct_2(A,B,B,D,F),k8_funct_2(B,B,F,C)) ) ) ) ) ) ) ) ).
fof(t44_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,A)
& m2_relset_1(C,B,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( v1_setwiseo(D,A)
=> ( k3_funcop_1(D,k2_funcop_1(B,k3_binop_1(A,D)),C) = C
& k3_funcop_1(D,C,k2_funcop_1(B,k3_binop_1(A,D))) = C ) ) ) ) ) ) ).
fof(t45_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ( v1_setwiseo(D,B)
=> k8_funcop_1(B,A,D,k3_binop_1(B,D),C) = C ) ) ) ) ) ).
fof(t46_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ( v1_setwiseo(D,B)
=> k7_funcop_1(B,A,D,C,k3_binop_1(B,D)) = C ) ) ) ) ) ).
fof(t47_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(D,A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(A,A),A)
& m2_relset_1(G,k2_zfmisc_1(A,A),A) )
=> ( r6_binop_1(A,F,G)
=> k3_finseqop(A,A,A,F,k2_binop_1(A,A,A,G,B,C),E) = k1_finseqop(A,A,A,G,k3_finseqop(A,A,A,F,B,E),k3_finseqop(A,A,A,F,C,E)) ) ) ) ) ) ) ) ) ).
fof(t48_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(D,A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(A,A),A)
& m2_relset_1(G,k2_zfmisc_1(A,A),A) )
=> ( r6_binop_1(A,F,G)
=> k2_finseqop(A,A,A,F,E,k2_binop_1(A,A,A,G,B,C)) = k1_finseqop(A,A,A,G,k2_finseqop(A,A,A,F,E,B),k2_finseqop(A,A,A,F,E,C)) ) ) ) ) ) ) ) ) ).
fof(t49_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( m2_finseq_2(E,B,k4_finseq_2(C,B))
=> ! [F] :
( m2_finseq_2(F,B,k4_finseq_2(C,B))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(B,B),B)
& m2_relset_1(G,k2_zfmisc_1(B,B),B) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(A,A),A)
& m2_relset_1(H,k2_zfmisc_1(A,A),A) )
=> ( ! [I] :
( m1_subset_1(I,B)
=> ! [J] :
( m1_subset_1(J,B)
=> k8_funct_2(B,A,D,k2_binop_1(B,B,B,G,I,J)) = k2_binop_1(A,A,A,H,k8_funct_2(B,A,D,I),k8_funct_2(B,A,D,J)) ) )
=> k5_finseqop(B,A,k1_finseqop(B,B,B,G,E,F),D) = k1_finseqop(A,A,A,H,k5_finseqop(B,A,E,D),k5_finseqop(B,A,F,D)) ) ) ) ) ) ) ) ) ) ).
fof(t50_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,A)
& m2_relset_1(E,B,A) )
=> ! [F] :
( m2_finseq_2(F,B,k4_finseq_2(D,B))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(B,B),B)
& m2_relset_1(G,k2_zfmisc_1(B,B),B) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(A,A),A)
& m2_relset_1(H,k2_zfmisc_1(A,A),A) )
=> ( ! [I] :
( m1_subset_1(I,B)
=> ! [J] :
( m1_subset_1(J,B)
=> k8_funct_2(B,A,E,k2_binop_1(B,B,B,G,I,J)) = k2_binop_1(A,A,A,H,k8_funct_2(B,A,E,I),k8_funct_2(B,A,E,J)) ) )
=> k5_finseqop(B,A,k3_finseqop(B,B,B,G,C,F),E) = k3_finseqop(A,A,A,H,k8_funct_2(B,A,E,C),k5_finseqop(B,A,F,E)) ) ) ) ) ) ) ) ) ) ).
fof(t51_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,A)
& m2_relset_1(E,B,A) )
=> ! [F] :
( m2_finseq_2(F,B,k4_finseq_2(D,B))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(B,B),B)
& m2_relset_1(G,k2_zfmisc_1(B,B),B) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(A,A),A)
& m2_relset_1(H,k2_zfmisc_1(A,A),A) )
=> ( ! [I] :
( m1_subset_1(I,B)
=> ! [J] :
( m1_subset_1(J,B)
=> k8_funct_2(B,A,E,k2_binop_1(B,B,B,G,I,J)) = k2_binop_1(A,A,A,H,k8_funct_2(B,A,E,I),k8_funct_2(B,A,E,J)) ) )
=> k5_finseqop(B,A,k2_finseqop(B,B,B,G,F,C),E) = k2_finseqop(A,A,A,H,k5_finseqop(B,A,F,E),k8_funct_2(B,A,E,C)) ) ) ) ) ) ) ) ) ) ).
fof(t52_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,A,k4_finseq_2(B,A))
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(B,A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,A)
& m2_relset_1(F,A,A) )
=> ( r7_binop_1(A,F,E)
=> k5_finseqop(A,A,k1_finseqop(A,A,A,E,C,D),F) = k1_finseqop(A,A,A,E,k5_finseqop(A,A,C,F),k5_finseqop(A,A,D,F)) ) ) ) ) ) ) ) ).
fof(t53_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(C,A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,A)
& m2_relset_1(F,A,A) )
=> ( r7_binop_1(A,F,E)
=> k5_finseqop(A,A,k3_finseqop(A,A,A,E,B,D),F) = k3_finseqop(A,A,A,E,k8_funct_2(A,A,F,B),k5_finseqop(A,A,D,F)) ) ) ) ) ) ) ) ).
fof(t54_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(C,A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,A)
& m2_relset_1(F,A,A) )
=> ( r7_binop_1(A,F,E)
=> k5_finseqop(A,A,k2_finseqop(A,A,A,E,D,B),F) = k2_finseqop(A,A,A,E,k5_finseqop(A,A,D,F),k8_funct_2(A,A,F,B)) ) ) ) ) ) ) ) ).
fof(t55_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,A)
& m2_relset_1(E,A,A) )
=> ( ( r6_binop_1(A,C,D)
& E = k8_funcop_1(A,A,C,B,k6_partfun1(A)) )
=> r7_binop_1(A,E,D) ) ) ) ) ) ) ).
fof(t56_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,A)
& m2_relset_1(E,A,A) )
=> ( ( r6_binop_1(A,C,D)
& E = k7_funcop_1(A,A,C,k6_partfun1(A),B) )
=> r7_binop_1(A,E,D) ) ) ) ) ) ) ).
fof(t57_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,A,k4_finseq_2(B,A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( v1_setwiseo(D,A)
=> ( k1_finseqop(A,A,A,D,k4_finseqop(A,B,k3_binop_1(A,D)),C) = C
& k1_finseqop(A,A,A,D,C,k4_finseqop(A,B,k3_binop_1(A,D))) = C ) ) ) ) ) ) ).
fof(t58_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,A,k4_finseq_2(B,A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( v1_setwiseo(D,A)
=> k3_finseqop(A,A,A,D,k3_binop_1(A,D),C) = C ) ) ) ) ) ).
fof(t59_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,A,k4_finseq_2(B,A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( v1_setwiseo(D,A)
=> k2_finseqop(A,A,A,D,C,k3_binop_1(A,D)) = C ) ) ) ) ) ).
fof(d1_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( r1_finseqop(A,B,C)
<=> ! [D] :
( m1_subset_1(D,A)
=> ( k2_binop_1(A,A,A,C,D,k8_funct_2(A,A,B,D)) = k3_binop_1(A,C)
& k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),D) = k3_binop_1(A,C) ) ) ) ) ) ) ).
fof(d2_finseqop,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) )
=> ( v1_finseqop(B,A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A)
& r1_finseqop(A,C,B) ) ) ) ) ).
fof(d3_finseqop,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) )
=> ( ( v1_setwiseo(B,A)
& v2_binop_1(B,A)
& v1_finseqop(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( C = k6_finseqop(A,B)
<=> r1_finseqop(A,C,B) ) ) ) ) ) ).
fof(t60_finseqop,axiom,
$true ).
fof(t61_finseqop,axiom,
$true ).
fof(t62_finseqop,axiom,
$true ).
fof(t63_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( ( v1_setwiseo(C,A)
& v2_binop_1(C,A)
& v1_finseqop(C,A) )
=> ( k2_binop_1(A,A,A,C,k8_funct_2(A,A,k6_finseqop(A,C),B),B) = k3_binop_1(A,C)
& k2_binop_1(A,A,A,C,B,k8_funct_2(A,A,k6_finseqop(A,C),B)) = k3_binop_1(A,C) ) ) ) ) ) ).
fof(t64_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( ( v1_setwiseo(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A)
& k2_binop_1(A,A,A,D,B,C) = k3_binop_1(A,D) )
=> ( B = k8_funct_2(A,A,k6_finseqop(A,D),C)
& k8_funct_2(A,A,k6_finseqop(A,D),B) = C ) ) ) ) ) ) ).
fof(t65_finseqop,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) )
=> ( ( v1_setwiseo(B,A)
& v2_binop_1(B,A)
& v1_finseqop(B,A) )
=> k8_funct_2(A,A,k6_finseqop(A,B),k3_binop_1(A,B)) = k3_binop_1(A,B) ) ) ) ).
fof(t66_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( ( v1_setwiseo(C,A)
& v2_binop_1(C,A)
& v1_finseqop(C,A) )
=> k8_funct_2(A,A,k6_finseqop(A,C),k8_funct_2(A,A,k6_finseqop(A,C),B)) = B ) ) ) ) ).
fof(t67_finseqop,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) )
=> ( ( v1_setwiseo(B,A)
& v2_binop_1(B,A)
& v1_binop_1(B,A)
& v1_finseqop(B,A) )
=> r7_binop_1(A,k6_finseqop(A,B),B) ) ) ) ).
fof(t68_finseqop,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] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ( ( v1_setwiseo(E,A)
& v2_binop_1(E,A)
& v1_finseqop(E,A) )
=> ( ( k2_binop_1(A,A,A,E,B,C) != k2_binop_1(A,A,A,E,B,D)
& k2_binop_1(A,A,A,E,C,B) != k2_binop_1(A,A,A,E,D,B) )
| C = D ) ) ) ) ) ) ) ).
fof(t69_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( ( v1_setwiseo(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A) )
=> ( ( k2_binop_1(A,A,A,D,B,C) != C
& k2_binop_1(A,A,A,D,C,B) != C )
| B = k3_binop_1(A,D) ) ) ) ) ) ) ).
fof(t70_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( ( v2_binop_1(C,A)
& v1_setwiseo(C,A)
& v1_finseqop(C,A)
& r6_binop_1(A,D,C)
& B = k3_binop_1(A,C) )
=> ! [E] :
( m1_subset_1(E,A)
=> ( k2_binop_1(A,A,A,D,B,E) = B
& k2_binop_1(A,A,A,D,E,B) = B ) ) ) ) ) ) ) ).
fof(t71_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,A)
& m2_relset_1(F,A,A) )
=> ( ( v1_setwiseo(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A)
& F = k6_finseqop(A,D)
& r6_binop_1(A,E,D) )
=> ( k8_funct_2(A,A,F,k2_binop_1(A,A,A,E,B,C)) = k2_binop_1(A,A,A,E,k8_funct_2(A,A,F,B),C)
& k8_funct_2(A,A,F,k2_binop_1(A,A,A,E,B,C)) = k2_binop_1(A,A,A,E,B,k8_funct_2(A,A,F,C)) ) ) ) ) ) ) ) ) ).
fof(t72_finseqop,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> ( ( v1_setwiseo(B,A)
& v2_binop_1(B,A)
& v1_finseqop(B,A)
& D = k6_finseqop(A,B)
& r6_binop_1(A,C,B)
& v1_setwiseo(C,A) )
=> k8_funcop_1(A,A,C,k8_funct_2(A,A,D,k3_binop_1(A,C)),k6_partfun1(A)) = D ) ) ) ) ) ).
fof(t73_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( ( v2_binop_1(C,A)
& v1_setwiseo(C,A)
& v1_finseqop(C,A)
& r6_binop_1(A,D,C) )
=> k8_funct_2(A,A,k8_funcop_1(A,A,D,B,k6_partfun1(A)),k3_binop_1(A,C)) = k3_binop_1(A,C) ) ) ) ) ) ).
fof(t74_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( ( v2_binop_1(C,A)
& v1_setwiseo(C,A)
& v1_finseqop(C,A)
& r6_binop_1(A,D,C) )
=> k8_funct_2(A,A,k7_funcop_1(A,A,D,k6_partfun1(A),B),k3_binop_1(A,C)) = k3_binop_1(A,C) ) ) ) ) ) ).
fof(t75_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,A)
& m2_relset_1(C,B,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( ( v1_setwiseo(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A) )
=> ( k6_funcop_1(A,B,D,C,k7_funct_2(B,A,A,C,k6_finseqop(A,D))) = k2_funcop_1(B,k3_binop_1(A,D))
& k6_funcop_1(A,B,D,k7_funct_2(B,A,A,C,k6_finseqop(A,D)),C) = k2_funcop_1(B,k3_binop_1(A,D)) ) ) ) ) ) ) ).
fof(t76_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,A)
& m2_relset_1(C,B,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ( ( v2_binop_1(E,A)
& v1_finseqop(E,A)
& v1_setwiseo(E,A)
& k6_funcop_1(A,B,E,C,D) = k2_funcop_1(B,k3_binop_1(A,E)) )
=> ( C = k7_funct_2(B,A,A,D,k6_finseqop(A,E))
& k7_funct_2(B,A,A,C,k6_finseqop(A,E)) = D ) ) ) ) ) ) ) ).
fof(t77_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,A,k4_finseq_2(B,A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ( ( v1_setwiseo(D,A)
& v2_binop_1(D,A)
& v1_finseqop(D,A) )
=> ( k1_finseqop(A,A,A,D,C,k5_finseqop(A,A,C,k6_finseqop(A,D))) = k4_finseqop(A,B,k3_binop_1(A,D))
& k1_finseqop(A,A,A,D,k5_finseqop(A,A,C,k6_finseqop(A,D)),C) = k4_finseqop(A,B,k3_binop_1(A,D)) ) ) ) ) ) ) ).
fof(t78_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,A,k4_finseq_2(B,A))
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(B,A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ( ( v2_binop_1(E,A)
& v1_finseqop(E,A)
& v1_setwiseo(E,A)
& k1_finseqop(A,A,A,E,C,D) = k4_finseqop(A,B,k3_binop_1(A,E)) )
=> ( C = k5_finseqop(A,A,D,k6_finseqop(A,E))
& k5_finseqop(A,A,C,k6_finseqop(A,E)) = D ) ) ) ) ) ) ) ).
fof(t79_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ( ( v2_binop_1(E,A)
& v1_setwiseo(E,A)
& C = k3_binop_1(A,E)
& v1_finseqop(E,A)
& r6_binop_1(A,F,E) )
=> k8_funcop_1(A,B,F,C,D) = k2_funcop_1(B,C) ) ) ) ) ) ) ) ).
fof(t80_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(C,A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,A),A)
& m2_relset_1(F,k2_zfmisc_1(A,A),A) )
=> ( ( v2_binop_1(E,A)
& v1_setwiseo(E,A)
& B = k3_binop_1(A,E)
& v1_finseqop(E,A)
& r6_binop_1(A,F,E) )
=> k3_finseqop(A,A,A,F,B,D) = k4_finseqop(A,C,B) ) ) ) ) ) ) ) ).
fof(d4_finseqop,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> k7_finseqop(A,B,C) = k5_relat_1(k15_funct_3(B,C),A) ) ) ) ).
fof(t81_finseqop,axiom,
$true ).
fof(t82_finseqop,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(k4_tarski(A,B),k1_relat_1(k7_finseqop(C,D,E)))
=> k1_funct_1(k7_finseqop(C,D,E),k4_tarski(A,B)) = k1_funct_1(C,k4_tarski(k1_funct_1(D,A),k1_funct_1(E,B))) ) ) ) ) ).
fof(t83_finseqop,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(k4_tarski(A,B),k1_relat_1(k7_finseqop(C,D,E)))
=> k1_binop_1(k7_finseqop(C,D,E),A,B) = k1_binop_1(C,k1_funct_1(D,A),k1_funct_1(E,B)) ) ) ) ) ).
fof(t84_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,B),C)
& m2_relset_1(F,k2_zfmisc_1(A,B),C) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,D,A)
& m2_relset_1(G,D,A) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,E,B)
& m2_relset_1(H,E,B) )
=> ( v1_funct_1(k7_finseqop(F,G,H))
& v1_funct_2(k7_finseqop(F,G,H),k2_zfmisc_1(D,E),C)
& m2_relset_1(k7_finseqop(F,G,H),k2_zfmisc_1(D,E),C) ) ) ) ) ) ) ) ) ) ).
fof(t85_finseqop,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> ( v1_funct_1(k7_finseqop(B,C,D))
& v1_funct_2(k7_finseqop(B,C,D),k2_zfmisc_1(A,A),A)
& m2_relset_1(k7_finseqop(B,C,D),k2_zfmisc_1(A,A),A) ) ) ) ) ) ).
fof(t86_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ! [F] :
( m1_subset_1(F,D)
=> ! [G] :
( m1_subset_1(G,E)
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(A,B),C)
& m2_relset_1(H,k2_zfmisc_1(A,B),C) )
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,D,A)
& m2_relset_1(I,D,A) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,E,B)
& m2_relset_1(J,E,B) )
=> k1_binop_1(k7_finseqop(H,I,J),F,G) = k2_binop_1(A,B,C,H,k8_funct_2(D,A,I,F),k8_funct_2(E,B,J,G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t87_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,A)
& m2_relset_1(E,A,A) )
=> ( k2_binop_1(A,A,A,k8_finseqop(A,D,k6_partfun1(A),E),B,C) = k2_binop_1(A,A,A,D,B,k8_funct_2(A,A,E,C))
& k2_binop_1(A,A,A,k8_finseqop(A,D,E,k6_partfun1(A)),B,C) = k2_binop_1(A,A,A,D,k8_funct_2(A,A,E,B),C) ) ) ) ) ) ) ).
fof(t88_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [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,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,B)
& m2_relset_1(F,B,B) )
=> k6_funcop_1(B,A,k8_finseqop(B,E,k6_partfun1(B),F),C,D) = k6_funcop_1(B,A,E,C,k7_funct_2(A,B,B,D,F)) ) ) ) ) ) ) ).
fof(t89_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,A,k4_finseq_2(B,A))
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(B,A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,A)
& m2_relset_1(F,A,A) )
=> k1_finseqop(A,A,A,k8_finseqop(A,E,k6_partfun1(A),F),C,D) = k1_finseqop(A,A,A,E,C,k5_finseqop(A,A,D,F)) ) ) ) ) ) ) ).
fof(t90_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,A)
& m2_relset_1(E,A,A) )
=> ( ( v2_binop_1(D,A)
& v1_setwiseo(D,A)
& v1_binop_1(D,A)
& v1_finseqop(D,A)
& E = k6_finseqop(A,D) )
=> ( k8_funct_2(A,A,E,k2_binop_1(A,A,A,k8_finseqop(A,D,k6_partfun1(A),E),B,C)) = k2_binop_1(A,A,A,k8_finseqop(A,D,E,k6_partfun1(A)),B,C)
& k2_binop_1(A,A,A,k8_finseqop(A,D,k6_partfun1(A),E),B,C) = k8_funct_2(A,A,E,k2_binop_1(A,A,A,k8_finseqop(A,D,E,k6_partfun1(A)),B,C)) ) ) ) ) ) ) ) ).
fof(t91_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( ( v2_binop_1(C,A)
& v1_setwiseo(C,A)
& v1_finseqop(C,A) )
=> k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),k6_finseqop(A,C)),B,B) = k3_binop_1(A,C) ) ) ) ) ).
fof(t92_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( ( v2_binop_1(C,A)
& v1_setwiseo(C,A)
& v1_finseqop(C,A) )
=> k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),k6_finseqop(A,C)),B,k3_binop_1(A,C)) = B ) ) ) ) ).
fof(t93_finseqop,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> ( ( v2_binop_1(C,A)
& v1_setwiseo(C,A)
& v1_finseqop(C,A)
& D = k6_finseqop(A,C) )
=> k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),D),k3_binop_1(A,C),B) = k8_funct_2(A,A,D,B) ) ) ) ) ) ).
fof(t94_finseqop,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( ( v1_binop_1(B,A)
& v2_binop_1(B,A)
& v1_setwiseo(B,A)
& v1_finseqop(B,A)
& C = k8_finseqop(A,B,k6_partfun1(A),k6_finseqop(A,B)) )
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,F,G)) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,G)) ) ) ) ) ) ) ) ) ).
fof(dt_k1_finseqop,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C)
& m1_finseq_1(E,A)
& m1_finseq_1(F,B) )
=> m2_finseq_1(k1_finseqop(A,B,C,D,E,F),C) ) ).
fof(redefinition_k1_finseqop,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C)
& m1_finseq_1(E,A)
& m1_finseq_1(F,B) )
=> k1_finseqop(A,B,C,D,E,F) = k3_funcop_1(D,E,F) ) ).
fof(dt_k2_finseqop,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C)
& m1_finseq_1(E,A)
& m1_subset_1(F,B) )
=> m2_finseq_1(k2_finseqop(A,B,C,D,E,F),C) ) ).
fof(redefinition_k2_finseqop,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C)
& m1_finseq_1(E,A)
& m1_subset_1(F,B) )
=> k2_finseqop(A,B,C,D,E,F) = k4_funcop_1(D,E,F) ) ).
fof(dt_k3_finseqop,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C)
& m1_subset_1(E,A)
& m1_finseq_1(F,B) )
=> m2_finseq_1(k3_finseqop(A,B,C,D,E,F),C) ) ).
fof(redefinition_k3_finseqop,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C)
& m1_subset_1(E,A)
& m1_finseq_1(F,B) )
=> k3_finseqop(A,B,C,D,E,F) = k5_funcop_1(D,E,F) ) ).
fof(dt_k4_finseqop,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,A) )
=> m2_finseq_2(k4_finseqop(A,B,C),A,k4_finseq_2(B,A)) ) ).
fof(redefinition_k4_finseqop,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,A) )
=> k4_finseqop(A,B,C) = k2_finseq_2(B,C) ) ).
fof(dt_k5_finseqop,axiom,
! [A,B,C,D] :
( ( m1_finseq_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,A,B)
& m1_relset_1(D,A,B) )
=> m2_finseq_1(k5_finseqop(A,B,C,D),B) ) ).
fof(redefinition_k5_finseqop,axiom,
! [A,B,C,D] :
( ( m1_finseq_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,A,B)
& m1_relset_1(D,A,B) )
=> k5_finseqop(A,B,C,D) = k5_relat_1(C,D) ) ).
fof(dt_k6_finseqop,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ( v1_funct_1(k6_finseqop(A,B))
& v1_funct_2(k6_finseqop(A,B),A,A)
& m2_relset_1(k6_finseqop(A,B),A,A) ) ) ).
fof(dt_k7_finseqop,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_relat_1(C)
& v1_funct_1(C) )
=> ( v1_relat_1(k7_finseqop(A,B,C))
& v1_funct_1(k7_finseqop(A,B,C)) ) ) ).
fof(dt_k8_finseqop,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& m1_relset_1(C,A,A)
& v1_funct_1(D)
& v1_funct_2(D,A,A)
& m1_relset_1(D,A,A) )
=> ( v1_funct_1(k8_finseqop(A,B,C,D))
& v1_funct_2(k8_finseqop(A,B,C,D),k2_zfmisc_1(A,A),A)
& m2_relset_1(k8_finseqop(A,B,C,D),k2_zfmisc_1(A,A),A) ) ) ).
fof(redefinition_k8_finseqop,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& m1_relset_1(C,A,A)
& v1_funct_1(D)
& v1_funct_2(D,A,A)
& m1_relset_1(D,A,A) )
=> k8_finseqop(A,B,C,D) = k7_finseqop(B,C,D) ) ).
%------------------------------------------------------------------------------