SET007 Axioms: SET007+143.ax
%------------------------------------------------------------------------------
% File : SET007+143 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Property of Complex Functions
% 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 : cfunct_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 101 ( 12 unt; 0 def)
% Number of atoms : 645 ( 93 equ)
% Maximal formula atoms : 23 ( 6 avg)
% Number of connectives : 636 ( 92 ~; 0 |; 223 &)
% ( 9 <=>; 312 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 33 ( 33 usr; 5 con; 0-4 aty)
% Number of variables : 311 ( 310 !; 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(d1_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ( D = k1_cfunct_1(A,B,C)
<=> ( k4_relset_1(A,k2_numbers,D) = k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k6_subset_1(A,k4_relset_1(A,k2_numbers,C),k11_relset_1(A,k2_numbers,C,k1_tarski(np__0))))
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k4_relset_1(A,k2_numbers,D))
=> k4_finseq_4(A,k2_numbers,D,E) = k9_complex1(k4_finseq_4(A,k2_numbers,B,E),k12_complex1(k4_finseq_4(A,k2_numbers,C,E))) ) ) ) ) ) ) ) ) ).
fof(d2_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( C = k2_cfunct_1(A,B)
<=> ( k4_relset_1(A,k2_numbers,C) = k6_subset_1(A,k4_relset_1(A,k2_numbers,B),k11_relset_1(A,k2_numbers,B,k1_tarski(np__0)))
& ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,k4_relset_1(A,k2_numbers,C))
=> k4_finseq_4(A,k2_numbers,C,D) = k12_complex1(k4_finseq_4(A,k2_numbers,B,D)) ) ) ) ) ) ) ) ).
fof(t1_cfunct_1,axiom,
$true ).
fof(t2_cfunct_1,axiom,
$true ).
fof(t3_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( k4_relset_1(A,k2_numbers,k2_comseq_1(A,B,C)) = k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k4_relset_1(A,k2_numbers,C))
& ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,k4_relset_1(A,k2_numbers,k2_comseq_1(A,B,C)))
=> k4_finseq_4(A,k2_numbers,k2_comseq_1(A,B,C),D) = k8_complex1(k4_finseq_4(A,k2_numbers,B,D),k4_finseq_4(A,k2_numbers,C,D)) ) ) ) ) ) ) ).
fof(t4_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( k4_relset_1(A,k2_numbers,k6_comseq_1(A,B,C)) = k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k4_relset_1(A,k2_numbers,C))
& ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,k4_relset_1(A,k2_numbers,k6_comseq_1(A,B,C)))
=> k4_finseq_4(A,k2_numbers,k6_comseq_1(A,B,C),D) = k11_complex1(k4_finseq_4(A,k2_numbers,B,D),k4_finseq_4(A,k2_numbers,C,D)) ) ) ) ) ) ) ).
fof(t5_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( k4_relset_1(A,k2_numbers,k3_comseq_1(A,B,C)) = k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k4_relset_1(A,k2_numbers,C))
& ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,k4_relset_1(A,k2_numbers,k3_comseq_1(A,B,C)))
=> k4_finseq_4(A,k2_numbers,k3_comseq_1(A,B,C),D) = k9_complex1(k4_finseq_4(A,k2_numbers,B,D),k4_finseq_4(A,k2_numbers,C,D)) ) ) ) ) ) ) ).
fof(t6_cfunct_1,axiom,
$true ).
fof(t7_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( k4_relset_1(A,k2_numbers,k4_comseq_1(A,B,C)) = k4_relset_1(A,k2_numbers,B)
& ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,k4_relset_1(A,k2_numbers,k4_comseq_1(A,B,C)))
=> k4_finseq_4(A,k2_numbers,k4_comseq_1(A,B,C),D) = k9_complex1(C,k4_finseq_4(A,k2_numbers,B,D)) ) ) ) ) ) ) ).
fof(t8_cfunct_1,axiom,
$true ).
fof(t9_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ( k4_relset_1(A,k2_numbers,k5_comseq_1(A,B)) = k4_relset_1(A,k2_numbers,B)
& ! [C] :
( m1_subset_1(C,A)
=> ( r2_hidden(C,k4_relset_1(A,k2_numbers,k5_comseq_1(A,B)))
=> k4_finseq_4(A,k2_numbers,k5_comseq_1(A,B),C) = k10_complex1(k4_finseq_4(A,k2_numbers,B,C)) ) ) ) ) ) ).
fof(t10_cfunct_1,axiom,
$true ).
fof(t11_cfunct_1,axiom,
$true ).
fof(t12_cfunct_1,axiom,
$true ).
fof(t13_cfunct_1,axiom,
$true ).
fof(t14_cfunct_1,axiom,
$true ).
fof(t15_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ( r1_tarski(k4_relset_1(A,k2_numbers,k2_cfunct_1(A,B)),k4_relset_1(A,k2_numbers,B))
& k5_subset_1(A,k4_relset_1(A,k2_numbers,B),k6_subset_1(A,k4_relset_1(A,k2_numbers,B),k11_relset_1(A,k2_numbers,B,k1_tarski(np__0)))) = k6_subset_1(A,k4_relset_1(A,k2_numbers,B),k11_relset_1(A,k2_numbers,B,k1_tarski(np__0))) ) ) ) ).
fof(t16_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> k6_subset_1(A,k4_relset_1(A,k2_numbers,k3_comseq_1(A,B,C)),k11_relset_1(A,k2_numbers,k3_comseq_1(A,B,C),k1_tarski(np__0))) = k5_subset_1(A,k6_subset_1(A,k4_relset_1(A,k2_numbers,B),k11_relset_1(A,k2_numbers,B,k1_tarski(np__0))),k6_subset_1(A,k4_relset_1(A,k2_numbers,C),k11_relset_1(A,k2_numbers,C,k1_tarski(np__0)))) ) ) ) ).
fof(t17_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ~ ( r2_hidden(B,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,C)))
& k4_finseq_4(A,k2_numbers,C,B) = np__0 ) ) ) ) ).
fof(t18_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> k11_relset_1(A,k2_numbers,k2_cfunct_1(A,B),k1_tarski(np__0)) = k1_xboole_0 ) ) ).
fof(t19_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ( k11_relset_1(A,k1_numbers,k9_comseq_1(A,B),k1_tarski(np__0)) = k11_relset_1(A,k2_numbers,B,k1_tarski(np__0))
& k11_relset_1(A,k2_numbers,k5_comseq_1(A,B),k1_tarski(np__0)) = k11_relset_1(A,k2_numbers,B,k1_tarski(np__0)) ) ) ) ).
fof(t20_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> k4_relset_1(A,k2_numbers,k2_cfunct_1(A,k2_cfunct_1(A,B))) = k4_relset_1(A,k2_numbers,k2_partfun1(A,k2_numbers,B,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,B)))) ) ) ).
fof(t21_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( C != np__0
=> k11_relset_1(A,k2_numbers,k4_comseq_1(A,B,C),k1_tarski(np__0)) = k11_relset_1(A,k2_numbers,B,k1_tarski(np__0)) ) ) ) ) ).
fof(t22_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k2_comseq_1(A,k2_comseq_1(A,B,C),D) = k2_comseq_1(A,B,k2_comseq_1(A,C,D)) ) ) ) ) ).
fof(t23_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k3_comseq_1(A,k3_comseq_1(A,B,C),D) = k3_comseq_1(A,B,k3_comseq_1(A,C,D)) ) ) ) ) ).
fof(t24_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k3_comseq_1(A,k2_comseq_1(A,B,C),D) = k2_comseq_1(A,k3_comseq_1(A,B,D),k3_comseq_1(A,C,D)) ) ) ) ) ).
fof(t25_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k3_comseq_1(A,B,k2_comseq_1(A,C,D)) = k2_comseq_1(A,k3_comseq_1(A,B,C),k3_comseq_1(A,B,D)) ) ) ) ) ).
fof(t26_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k4_comseq_1(A,k3_comseq_1(A,B,C),D) = k3_comseq_1(A,k4_comseq_1(A,B,D),C) ) ) ) ) ).
fof(t27_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k4_comseq_1(A,k3_comseq_1(A,B,C),D) = k3_comseq_1(A,B,k4_comseq_1(A,C,D)) ) ) ) ) ).
fof(t28_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k3_comseq_1(A,k6_comseq_1(A,B,C),D) = k6_comseq_1(A,k3_comseq_1(A,B,D),k3_comseq_1(A,C,D)) ) ) ) ) ).
fof(t29_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k6_comseq_1(A,k3_comseq_1(A,B,C),k3_comseq_1(A,B,D)) = k3_comseq_1(A,B,k6_comseq_1(A,C,D)) ) ) ) ) ).
fof(t30_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k4_comseq_1(A,k2_comseq_1(A,B,C),D) = k2_comseq_1(A,k4_comseq_1(A,B,D),k4_comseq_1(A,C,D)) ) ) ) ) ).
fof(t31_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k4_comseq_1(A,B,k9_complex1(C,D)) = k4_comseq_1(A,k4_comseq_1(A,B,D),C) ) ) ) ) ).
fof(t32_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k4_comseq_1(A,k6_comseq_1(A,B,C),D) = k6_comseq_1(A,k4_comseq_1(A,B,D),k4_comseq_1(A,C,D)) ) ) ) ) ).
fof(t33_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> k6_comseq_1(A,B,C) = k4_comseq_1(A,k6_comseq_1(A,C,B),k10_complex1(k6_complex1)) ) ) ) ).
fof(t34_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k6_comseq_1(A,B,k2_comseq_1(A,C,D)) = k6_comseq_1(A,k6_comseq_1(A,B,C),D) ) ) ) ) ).
fof(t35_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> k4_comseq_1(A,B,k6_complex1) = B ) ) ).
fof(t36_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k6_comseq_1(A,B,k6_comseq_1(A,C,D)) = k2_comseq_1(A,k6_comseq_1(A,B,C),D) ) ) ) ) ).
fof(t37_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k2_comseq_1(A,B,k6_comseq_1(A,C,D)) = k6_comseq_1(A,k2_comseq_1(A,B,C),D) ) ) ) ) ).
fof(t38_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> k9_comseq_1(A,k3_comseq_1(A,B,C)) = k8_seq_1(A,k1_numbers,k9_comseq_1(A,B),k9_comseq_1(A,C)) ) ) ) ).
fof(t39_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k9_comseq_1(A,k4_comseq_1(A,B,C)) = k13_seq_1(A,k1_numbers,k9_comseq_1(A,B),k17_complex1(C)) ) ) ) ).
fof(t40_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> k5_comseq_1(A,B) = k4_comseq_1(A,B,k10_complex1(k6_complex1)) ) ) ).
fof(t41_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> k5_comseq_1(A,k5_comseq_1(A,B)) = B ) ) ).
fof(t42_cfunct_1,axiom,
$true ).
fof(t43_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> k6_comseq_1(A,B,k5_comseq_1(A,C)) = k2_comseq_1(A,B,C) ) ) ) ).
fof(t44_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> k2_cfunct_1(A,k2_cfunct_1(A,B)) = k2_partfun1(A,k2_numbers,B,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,B))) ) ) ).
fof(t45_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> k2_cfunct_1(A,k3_comseq_1(A,B,C)) = k3_comseq_1(A,k2_cfunct_1(A,B),k2_cfunct_1(A,C)) ) ) ) ).
fof(t46_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( C != np__0
=> k2_cfunct_1(A,k4_comseq_1(A,B,C)) = k4_comseq_1(A,k2_cfunct_1(A,B),k12_complex1(C)) ) ) ) ) ).
fof(t47_cfunct_1,axiom,
$true ).
fof(t48_cfunct_1,axiom,
$true ).
fof(t49_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> k2_cfunct_1(A,k5_comseq_1(A,B)) = k4_comseq_1(A,k2_cfunct_1(A,B),k10_complex1(k6_complex1)) ) ) ).
fof(t50_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> k4_rfunct_1(A,k1_numbers,k9_comseq_1(A,B)) = k9_comseq_1(A,k2_cfunct_1(A,B)) ) ) ).
fof(t51_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> k1_cfunct_1(A,B,C) = k3_comseq_1(A,B,k2_cfunct_1(A,C)) ) ) ) ).
fof(t52_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k4_comseq_1(A,k1_cfunct_1(A,B,C),D) = k1_cfunct_1(A,k4_comseq_1(A,B,D),C) ) ) ) ) ).
fof(t53_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> k3_comseq_1(A,k1_cfunct_1(A,B,C),C) = k2_partfun1(A,k2_numbers,B,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,C))) ) ) ) ).
fof(t54_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k2_numbers) )
=> k3_comseq_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,E)) = k1_cfunct_1(A,k3_comseq_1(A,B,D),k3_comseq_1(A,C,E)) ) ) ) ) ) ).
fof(t55_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> k2_cfunct_1(A,k1_cfunct_1(A,B,C)) = k1_cfunct_1(A,k2_partfun1(A,k2_numbers,C,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,C))),B) ) ) ) ).
fof(t56_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k3_comseq_1(A,B,k1_cfunct_1(A,C,D)) = k1_cfunct_1(A,k3_comseq_1(A,B,C),D) ) ) ) ) ).
fof(t57_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> k1_cfunct_1(A,B,k1_cfunct_1(A,C,D)) = k1_cfunct_1(A,k3_comseq_1(A,B,k2_partfun1(A,k2_numbers,D,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,D)))),C) ) ) ) ) ).
fof(t58_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( k5_comseq_1(A,k1_cfunct_1(A,B,C)) = k1_cfunct_1(A,k5_comseq_1(A,B),C)
& k1_cfunct_1(A,B,k5_comseq_1(A,C)) = k5_comseq_1(A,k1_cfunct_1(A,B,C)) ) ) ) ) ).
fof(t59_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ( k2_comseq_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,C)) = k1_cfunct_1(A,k2_comseq_1(A,B,D),C)
& k6_comseq_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,C)) = k1_cfunct_1(A,k6_comseq_1(A,B,D),C) ) ) ) ) ) ).
fof(t60_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k2_numbers) )
=> k2_comseq_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,E)) = k1_cfunct_1(A,k2_comseq_1(A,k3_comseq_1(A,B,E),k3_comseq_1(A,D,C)),k3_comseq_1(A,C,E)) ) ) ) ) ) ).
fof(t61_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k2_numbers) )
=> k1_cfunct_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,E)) = k1_cfunct_1(A,k3_comseq_1(A,B,k2_partfun1(A,k2_numbers,E,k4_relset_1(A,k2_numbers,k2_cfunct_1(A,E)))),k3_comseq_1(A,C,D)) ) ) ) ) ) ).
fof(t62_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,A,k2_numbers) )
=> k6_comseq_1(A,k1_cfunct_1(A,B,C),k1_cfunct_1(A,D,E)) = k1_cfunct_1(A,k6_comseq_1(A,k3_comseq_1(A,B,E),k3_comseq_1(A,D,C)),k3_comseq_1(A,C,E)) ) ) ) ) ) ).
fof(t63_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> k9_comseq_1(A,k1_cfunct_1(A,B,C)) = k2_rfunct_1(A,k1_numbers,k9_comseq_1(A,B),k9_comseq_1(A,C)) ) ) ) ).
fof(t64_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k2_numbers) )
=> ( k2_partfun1(B,k2_numbers,k2_comseq_1(B,C,D),A) = k2_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),k2_partfun1(B,k2_numbers,D,A))
& k2_partfun1(B,k2_numbers,k2_comseq_1(B,C,D),A) = k2_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),D)
& k2_partfun1(B,k2_numbers,k2_comseq_1(B,C,D),A) = k2_comseq_1(B,C,k2_partfun1(B,k2_numbers,D,A)) ) ) ) ) ).
fof(t65_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k2_numbers) )
=> ( k2_partfun1(B,k2_numbers,k3_comseq_1(B,C,D),A) = k3_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),k2_partfun1(B,k2_numbers,D,A))
& k2_partfun1(B,k2_numbers,k3_comseq_1(B,C,D),A) = k3_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),D)
& k2_partfun1(B,k2_numbers,k3_comseq_1(B,C,D),A) = k3_comseq_1(B,C,k2_partfun1(B,k2_numbers,D,A)) ) ) ) ) ).
fof(t66_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ( k2_partfun1(B,k2_numbers,k5_comseq_1(B,C),A) = k5_comseq_1(B,k2_partfun1(B,k2_numbers,C,A))
& k2_partfun1(B,k2_numbers,k2_cfunct_1(B,C),A) = k2_cfunct_1(B,k2_partfun1(B,k2_numbers,C,A))
& k2_partfun1(B,k1_numbers,k9_comseq_1(B,C),A) = k9_comseq_1(B,k2_partfun1(B,k2_numbers,C,A)) ) ) ) ).
fof(t67_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k2_numbers) )
=> ( k2_partfun1(B,k2_numbers,k6_comseq_1(B,C,D),A) = k6_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),k2_partfun1(B,k2_numbers,D,A))
& k2_partfun1(B,k2_numbers,k6_comseq_1(B,C,D),A) = k6_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),D)
& k2_partfun1(B,k2_numbers,k6_comseq_1(B,C,D),A) = k6_comseq_1(B,C,k2_partfun1(B,k2_numbers,D,A)) ) ) ) ) ).
fof(t68_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,B,k2_numbers) )
=> ( k2_partfun1(B,k2_numbers,k1_cfunct_1(B,C,D),A) = k1_cfunct_1(B,k2_partfun1(B,k2_numbers,C,A),k2_partfun1(B,k2_numbers,D,A))
& k2_partfun1(B,k2_numbers,k1_cfunct_1(B,C,D),A) = k1_cfunct_1(B,k2_partfun1(B,k2_numbers,C,A),D)
& k2_partfun1(B,k2_numbers,k1_cfunct_1(B,C,D),A) = k1_cfunct_1(B,C,k2_partfun1(B,k2_numbers,D,A)) ) ) ) ) ).
fof(t69_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k2_partfun1(B,k2_numbers,k4_comseq_1(B,C,D),A) = k4_comseq_1(B,k2_partfun1(B,k2_numbers,C,A),D) ) ) ) ).
fof(t70_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( ( ( v1_partfun1(B,A,k2_numbers)
& v1_partfun1(C,A,k2_numbers) )
=> v1_partfun1(k2_comseq_1(A,B,C),A,k2_numbers) )
& ( v1_partfun1(k2_comseq_1(A,B,C),A,k2_numbers)
=> ( v1_partfun1(B,A,k2_numbers)
& v1_partfun1(C,A,k2_numbers) ) )
& ( ( v1_partfun1(B,A,k2_numbers)
& v1_partfun1(C,A,k2_numbers) )
=> v1_partfun1(k6_comseq_1(A,B,C),A,k2_numbers) )
& ( v1_partfun1(k6_comseq_1(A,B,C),A,k2_numbers)
=> ( v1_partfun1(B,A,k2_numbers)
& v1_partfun1(C,A,k2_numbers) ) )
& ( ( v1_partfun1(B,A,k2_numbers)
& v1_partfun1(C,A,k2_numbers) )
=> v1_partfun1(k3_comseq_1(A,B,C),A,k2_numbers) )
& ( v1_partfun1(k3_comseq_1(A,B,C),A,k2_numbers)
=> ( v1_partfun1(B,A,k2_numbers)
& v1_partfun1(C,A,k2_numbers) ) ) ) ) ) ) ).
fof(t71_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( v1_partfun1(B,A,k2_numbers)
<=> v1_partfun1(k4_comseq_1(A,B,C),A,k2_numbers) ) ) ) ) ).
fof(t72_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ( v1_partfun1(B,A,k2_numbers)
<=> v1_partfun1(k5_comseq_1(A,B),A,k2_numbers) ) ) ) ).
fof(t73_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ( v1_partfun1(B,A,k2_numbers)
<=> v1_partfun1(k9_comseq_1(A,B),A,k1_numbers) ) ) ) ).
fof(t74_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ( v1_partfun1(k2_cfunct_1(A,B),A,k2_numbers)
<=> ( k11_relset_1(A,k2_numbers,B,k1_tarski(np__0)) = k1_xboole_0
& v1_partfun1(B,A,k2_numbers) ) ) ) ) ).
fof(t75_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( ( v1_partfun1(B,A,k2_numbers)
& k11_relset_1(A,k2_numbers,C,k1_tarski(np__0)) = k1_xboole_0
& v1_partfun1(C,A,k2_numbers) )
<=> v1_partfun1(k1_cfunct_1(A,B,C),A,k2_numbers) ) ) ) ) ).
fof(t76_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ( ( v1_partfun1(C,A,k2_numbers)
& v1_partfun1(D,A,k2_numbers) )
=> ( k4_finseq_4(A,k2_numbers,k2_comseq_1(A,C,D),B) = k8_complex1(k4_finseq_4(A,k2_numbers,C,B),k4_finseq_4(A,k2_numbers,D,B))
& k4_finseq_4(A,k2_numbers,k6_comseq_1(A,C,D),B) = k11_complex1(k4_finseq_4(A,k2_numbers,C,B),k4_finseq_4(A,k2_numbers,D,B))
& k4_finseq_4(A,k2_numbers,k3_comseq_1(A,C,D),B) = k9_complex1(k4_finseq_4(A,k2_numbers,C,B),k4_finseq_4(A,k2_numbers,D,B)) ) ) ) ) ) ) ).
fof(t77_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ( v1_partfun1(C,A,k2_numbers)
=> k4_finseq_4(A,k2_numbers,k4_comseq_1(A,C,D),B) = k9_complex1(D,k4_finseq_4(A,k2_numbers,C,B)) ) ) ) ) ) ).
fof(t78_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( v1_partfun1(C,A,k2_numbers)
=> ( k4_finseq_4(A,k2_numbers,k5_comseq_1(A,C),B) = k10_complex1(k4_finseq_4(A,k2_numbers,C,B))
& k2_seq_1(A,k1_numbers,k9_comseq_1(A,C),B) = k17_complex1(k4_finseq_4(A,k2_numbers,C,B)) ) ) ) ) ) ).
fof(t79_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ( v1_partfun1(k2_cfunct_1(A,C),A,k2_numbers)
=> k4_finseq_4(A,k2_numbers,k2_cfunct_1(A,C),B) = k12_complex1(k4_finseq_4(A,k2_numbers,C,B)) ) ) ) ) ).
fof(t80_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k2_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k2_numbers) )
=> ( ( v1_partfun1(C,A,k2_numbers)
& v1_partfun1(k2_cfunct_1(A,D),A,k2_numbers) )
=> k4_finseq_4(A,k2_numbers,k1_cfunct_1(A,C,D),B) = k9_complex1(k4_finseq_4(A,k2_numbers,C,B),k12_complex1(k4_finseq_4(A,k2_numbers,D,B))) ) ) ) ) ) ).
fof(d3_cfunct_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k2_numbers) )
=> ! [C] :
( r1_cfunct_1(A,B,C)
<=> r3_rfunct_1(k9_comseq_1(A,B),C) ) ) ) ).
fof(t81_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ( r1_cfunct_1(B,C,A)
<=> ? [D] :
( v1_xreal_0(D)
& ! [E] :
( m1_subset_1(E,B)
=> ( r2_hidden(E,k3_xboole_0(A,k4_relset_1(B,k2_numbers,C)))
=> r1_xreal_0(k17_complex1(k4_finseq_4(B,k2_numbers,C,E)),D) ) ) ) ) ) ) ).
fof(t82_cfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,C,k2_numbers) )
=> ( ( r1_tarski(A,B)
& r1_cfunct_1(C,D,B) )
=> r1_cfunct_1(C,D,A) ) ) ) ).
fof(t83_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ( r1_xboole_0(A,k4_relset_1(B,k2_numbers,C))
=> r1_cfunct_1(B,C,A) ) ) ) ).
fof(t84_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ( r1_cfunct_1(B,C,A)
=> r1_cfunct_1(B,k4_comseq_1(B,C,D),A) ) ) ) ) ).
fof(t85_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> r2_rfunct_1(k9_comseq_1(B,C),A) ) ) ).
fof(t86_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ( r1_cfunct_1(B,C,A)
=> ( r3_rfunct_1(k9_comseq_1(B,C),A)
& r1_cfunct_1(B,k5_comseq_1(B,C),A) ) ) ) ) ).
fof(t87_cfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,C,k2_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,k2_numbers) )
=> ( ( r1_cfunct_1(C,D,A)
& r1_cfunct_1(C,E,B) )
=> r1_cfunct_1(C,k2_comseq_1(C,D,E),k3_xboole_0(A,B)) ) ) ) ) ).
fof(t88_cfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,C,k2_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,k2_numbers) )
=> ( ( r1_cfunct_1(C,D,A)
& r1_cfunct_1(C,E,B) )
=> ( r1_cfunct_1(C,k3_comseq_1(C,D,E),k3_xboole_0(A,B))
& r1_cfunct_1(C,k6_comseq_1(C,D,E),k3_xboole_0(A,B)) ) ) ) ) ) ).
fof(t89_cfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,C,k2_numbers) )
=> ( ( r1_cfunct_1(C,D,A)
& r1_cfunct_1(C,D,B) )
=> r1_cfunct_1(C,D,k2_xboole_0(A,B)) ) ) ) ).
fof(t90_cfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,C,k2_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,k2_numbers) )
=> ( ( r1_partfun2(C,k2_numbers,D,A)
& r1_partfun2(C,k2_numbers,E,B) )
=> ( r1_partfun2(C,k2_numbers,k2_comseq_1(C,D,E),k3_xboole_0(A,B))
& r1_partfun2(C,k2_numbers,k6_comseq_1(C,D,E),k3_xboole_0(A,B))
& r1_partfun2(C,k2_numbers,k3_comseq_1(C,D,E),k3_xboole_0(A,B)) ) ) ) ) ) ).
fof(t91_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ( r1_partfun2(B,k2_numbers,C,A)
=> r1_partfun2(B,k2_numbers,k4_comseq_1(B,C,D),A) ) ) ) ) ).
fof(t92_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ( r1_partfun2(B,k2_numbers,C,A)
=> ( r1_partfun2(B,k1_numbers,k9_comseq_1(B,C),A)
& r1_partfun2(B,k2_numbers,k5_comseq_1(B,C),A) ) ) ) ) ).
fof(t93_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ( r1_partfun2(B,k2_numbers,C,A)
=> r1_cfunct_1(B,C,A) ) ) ) ).
fof(t94_cfunct_1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,B,k2_numbers) )
=> ( r1_partfun2(B,k2_numbers,C,A)
=> ( ! [D] :
( m1_subset_1(D,k2_numbers)
=> r1_cfunct_1(B,k4_comseq_1(B,C,D),A) )
& r1_cfunct_1(B,k5_comseq_1(B,C),A)
& r3_rfunct_1(k9_comseq_1(B,C),A) ) ) ) ) ).
fof(t95_cfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,C,k2_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,k2_numbers) )
=> ( ( r1_cfunct_1(C,D,A)
& r1_partfun2(C,k2_numbers,E,B) )
=> r1_cfunct_1(C,k2_comseq_1(C,D,E),k3_xboole_0(A,B)) ) ) ) ) ).
fof(t96_cfunct_1,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,C,k2_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,C,k2_numbers) )
=> ( ( r1_cfunct_1(C,D,A)
& r1_partfun2(C,k2_numbers,E,B) )
=> ( r1_cfunct_1(C,k6_comseq_1(C,D,E),k3_xboole_0(A,B))
& r1_cfunct_1(C,k6_comseq_1(C,E,D),k3_xboole_0(A,B))
& r1_cfunct_1(C,k3_comseq_1(C,D,E),k3_xboole_0(A,B)) ) ) ) ) ) ).
fof(dt_k1_cfunct_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k2_numbers)
& v1_funct_1(C)
& m1_relset_1(C,A,k2_numbers) )
=> ( v1_funct_1(k1_cfunct_1(A,B,C))
& m2_relset_1(k1_cfunct_1(A,B,C),A,k2_numbers) ) ) ).
fof(dt_k2_cfunct_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k2_numbers) )
=> ( v1_funct_1(k2_cfunct_1(A,B))
& m2_relset_1(k2_cfunct_1(A,B),A,k2_numbers) ) ) ).
%------------------------------------------------------------------------------