SET007 Axioms: SET007+50.ax
%------------------------------------------------------------------------------
% File : SET007+50 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Binary Operations on Numbers
% 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 : binop_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 146 ( 10 unt; 0 def)
% Number of atoms : 535 ( 105 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 389 ( 0 ~; 0 |; 222 &)
% ( 24 <=>; 143 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 0 prp; 1-3 aty)
% Number of functors : 70 ( 70 usr; 34 con; 0-6 aty)
% Number of variables : 185 ( 185 !; 0 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_binop_2,axiom,
! [A] :
( m1_subset_1(A,k3_numbers)
=> ( v1_xcmplx_0(A)
& v1_xreal_0(A)
& v1_rat_1(A) ) ) ).
fof(fc1_binop_2,axiom,
( v1_funct_1(k27_binop_2)
& v1_funct_2(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& v1_binop_1(k27_binop_2,k2_numbers)
& v2_binop_1(k27_binop_2,k2_numbers) ) ).
fof(fc2_binop_2,axiom,
( v1_funct_1(k29_binop_2)
& v1_funct_2(k29_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& v1_binop_1(k29_binop_2,k2_numbers)
& v2_binop_1(k29_binop_2,k2_numbers) ) ).
fof(fc3_binop_2,axiom,
( v1_funct_1(k33_binop_2)
& v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& v1_binop_1(k33_binop_2,k1_numbers)
& v2_binop_1(k33_binop_2,k1_numbers) ) ).
fof(fc4_binop_2,axiom,
( v1_funct_1(k35_binop_2)
& v1_funct_2(k35_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& v1_binop_1(k35_binop_2,k1_numbers)
& v2_binop_1(k35_binop_2,k1_numbers) ) ).
fof(fc5_binop_2,axiom,
( v1_funct_1(k39_binop_2)
& v1_funct_2(k39_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& v1_binop_1(k39_binop_2,k3_numbers)
& v2_binop_1(k39_binop_2,k3_numbers) ) ).
fof(fc6_binop_2,axiom,
( v1_funct_1(k41_binop_2)
& v1_funct_2(k41_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& v1_binop_1(k41_binop_2,k3_numbers)
& v2_binop_1(k41_binop_2,k3_numbers) ) ).
fof(fc7_binop_2,axiom,
( v1_funct_1(k44_binop_2)
& v1_funct_2(k44_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
& v1_binop_1(k44_binop_2,k4_numbers)
& v2_binop_1(k44_binop_2,k4_numbers) ) ).
fof(fc8_binop_2,axiom,
( v1_funct_1(k46_binop_2)
& v1_funct_2(k46_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
& v1_binop_1(k46_binop_2,k4_numbers)
& v2_binop_1(k46_binop_2,k4_numbers) ) ).
fof(fc9_binop_2,axiom,
( v1_funct_1(k47_binop_2)
& v1_funct_2(k47_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& v1_binop_1(k47_binop_2,k5_numbers)
& v2_binop_1(k47_binop_2,k5_numbers) ) ).
fof(fc10_binop_2,axiom,
( v1_funct_1(k48_binop_2)
& v1_funct_2(k48_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& v1_binop_1(k48_binop_2,k5_numbers)
& v2_binop_1(k48_binop_2,k5_numbers) ) ).
fof(fc11_binop_2,axiom,
( v1_funct_1(k27_binop_2)
& v1_funct_2(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& v1_binop_1(k27_binop_2,k2_numbers)
& v2_binop_1(k27_binop_2,k2_numbers)
& v1_setwiseo(k27_binop_2,k2_numbers) ) ).
fof(fc12_binop_2,axiom,
( v1_funct_1(k33_binop_2)
& v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& v1_binop_1(k33_binop_2,k1_numbers)
& v2_binop_1(k33_binop_2,k1_numbers)
& v1_setwiseo(k33_binop_2,k1_numbers) ) ).
fof(fc13_binop_2,axiom,
( v1_funct_1(k39_binop_2)
& v1_funct_2(k39_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& v1_binop_1(k39_binop_2,k3_numbers)
& v2_binop_1(k39_binop_2,k3_numbers)
& v1_setwiseo(k39_binop_2,k3_numbers) ) ).
fof(fc14_binop_2,axiom,
( v1_funct_1(k44_binop_2)
& v1_funct_2(k44_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
& v1_binop_1(k44_binop_2,k4_numbers)
& v2_binop_1(k44_binop_2,k4_numbers)
& v1_setwiseo(k44_binop_2,k4_numbers) ) ).
fof(fc15_binop_2,axiom,
( v1_funct_1(k47_binop_2)
& v1_funct_2(k47_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& v1_binop_1(k47_binop_2,k5_numbers)
& v2_binop_1(k47_binop_2,k5_numbers)
& v1_setwiseo(k47_binop_2,k5_numbers) ) ).
fof(fc16_binop_2,axiom,
( v1_funct_1(k29_binop_2)
& v1_funct_2(k29_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& v1_binop_1(k29_binop_2,k2_numbers)
& v2_binop_1(k29_binop_2,k2_numbers)
& v1_setwiseo(k29_binop_2,k2_numbers) ) ).
fof(fc17_binop_2,axiom,
( v1_funct_1(k35_binop_2)
& v1_funct_2(k35_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& v1_binop_1(k35_binop_2,k1_numbers)
& v2_binop_1(k35_binop_2,k1_numbers)
& v1_setwiseo(k35_binop_2,k1_numbers) ) ).
fof(fc18_binop_2,axiom,
( v1_funct_1(k41_binop_2)
& v1_funct_2(k41_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& v1_binop_1(k41_binop_2,k3_numbers)
& v2_binop_1(k41_binop_2,k3_numbers)
& v1_setwiseo(k41_binop_2,k3_numbers) ) ).
fof(fc19_binop_2,axiom,
( v1_funct_1(k46_binop_2)
& v1_funct_2(k46_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
& v1_binop_1(k46_binop_2,k4_numbers)
& v2_binop_1(k46_binop_2,k4_numbers)
& v1_setwiseo(k46_binop_2,k4_numbers) ) ).
fof(fc20_binop_2,axiom,
( v1_funct_1(k48_binop_2)
& v1_funct_2(k48_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& v1_binop_1(k48_binop_2,k5_numbers)
& v2_binop_1(k48_binop_2,k5_numbers)
& v1_setwiseo(k48_binop_2,k5_numbers) ) ).
fof(d1_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_numbers,k2_numbers)
& m2_relset_1(A,k2_numbers,k2_numbers) )
=> ( A = k25_binop_2
<=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> k8_funct_2(k2_numbers,k2_numbers,A,B) = k1_binop_2(B) ) ) ) ).
fof(d2_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_numbers,k2_numbers)
& m2_relset_1(A,k2_numbers,k2_numbers) )
=> ( A = k26_binop_2
<=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> k8_funct_2(k2_numbers,k2_numbers,A,B) = k2_binop_2(B) ) ) ) ).
fof(d3_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )
=> ( A = k27_binop_2
<=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k3_binop_2(B,C) ) ) ) ) ).
fof(d4_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )
=> ( A = k28_binop_2
<=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k4_binop_2(B,C) ) ) ) ) ).
fof(d5_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )
=> ( A = k29_binop_2
<=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k5_binop_2(B,C) ) ) ) ) ).
fof(d6_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )
=> ( A = k30_binop_2
<=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k6_binop_2(B,C) ) ) ) ) ).
fof(d7_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k1_numbers,k1_numbers)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ( A = k31_binop_2
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> k8_funct_2(k1_numbers,k1_numbers,A,B) = k7_binop_2(B) ) ) ) ).
fof(d8_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k1_numbers,k1_numbers)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ( A = k32_binop_2
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> k8_funct_2(k1_numbers,k1_numbers,A,B) = k8_binop_2(B) ) ) ) ).
fof(d9_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
=> ( A = k33_binop_2
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k9_binop_2(B,C) ) ) ) ) ).
fof(d10_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
=> ( A = k34_binop_2
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k10_binop_2(B,C) ) ) ) ) ).
fof(d11_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
=> ( A = k35_binop_2
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k11_binop_2(B,C) ) ) ) ) ).
fof(d12_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
=> ( A = k36_binop_2
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k12_binop_2(B,C) ) ) ) ) ).
fof(d13_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k3_numbers,k3_numbers)
& m2_relset_1(A,k3_numbers,k3_numbers) )
=> ( A = k37_binop_2
<=> ! [B] :
( m1_subset_1(B,k3_numbers)
=> k8_funct_2(k3_numbers,k3_numbers,A,B) = k13_binop_2(B) ) ) ) ).
fof(d14_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k3_numbers,k3_numbers)
& m2_relset_1(A,k3_numbers,k3_numbers) )
=> ( A = k38_binop_2
<=> ! [B] :
( m1_subset_1(B,k3_numbers)
=> k8_funct_2(k3_numbers,k3_numbers,A,B) = k14_binop_2(B) ) ) ) ).
fof(d15_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )
=> ( A = k39_binop_2
<=> ! [B] :
( m1_subset_1(B,k3_numbers)
=> ! [C] :
( m1_subset_1(C,k3_numbers)
=> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k15_binop_2(B,C) ) ) ) ) ).
fof(d16_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )
=> ( A = k40_binop_2
<=> ! [B] :
( m1_subset_1(B,k3_numbers)
=> ! [C] :
( m1_subset_1(C,k3_numbers)
=> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k16_binop_2(B,C) ) ) ) ) ).
fof(d17_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )
=> ( A = k41_binop_2
<=> ! [B] :
( m1_subset_1(B,k3_numbers)
=> ! [C] :
( m1_subset_1(C,k3_numbers)
=> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k17_binop_2(B,C) ) ) ) ) ).
fof(d18_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )
=> ( A = k42_binop_2
<=> ! [B] :
( m1_subset_1(B,k3_numbers)
=> ! [C] :
( m1_subset_1(C,k3_numbers)
=> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k18_binop_2(B,C) ) ) ) ) ).
fof(d19_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_numbers,k4_numbers)
& m2_relset_1(A,k4_numbers,k4_numbers) )
=> ( A = k43_binop_2
<=> ! [B] :
( m1_subset_1(B,k4_numbers)
=> k8_funct_2(k4_numbers,k4_numbers,A,B) = k19_binop_2(B) ) ) ) ).
fof(d20_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
& m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) )
=> ( A = k44_binop_2
<=> ! [B] :
( m1_subset_1(B,k4_numbers)
=> ! [C] :
( m1_subset_1(C,k4_numbers)
=> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k20_binop_2(B,C) ) ) ) ) ).
fof(d21_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
& m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) )
=> ( A = k45_binop_2
<=> ! [B] :
( m1_subset_1(B,k4_numbers)
=> ! [C] :
( m1_subset_1(C,k4_numbers)
=> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k21_binop_2(B,C) ) ) ) ) ).
fof(d22_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
& m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) )
=> ( A = k46_binop_2
<=> ! [B] :
( m1_subset_1(B,k4_numbers)
=> ! [C] :
( m1_subset_1(C,k4_numbers)
=> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k22_binop_2(B,C) ) ) ) ) ).
fof(d23_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) )
=> ( A = k47_binop_2
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k23_binop_2(B,C) ) ) ) ) ).
fof(d24_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) )
=> ( A = k48_binop_2
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k24_binop_2(B,C) ) ) ) ) ).
fof(t1_binop_2,axiom,
k3_binop_1(k2_numbers,k27_binop_2) = np__0 ).
fof(t2_binop_2,axiom,
k3_binop_1(k1_numbers,k33_binop_2) = np__0 ).
fof(t3_binop_2,axiom,
k3_binop_1(k3_numbers,k39_binop_2) = np__0 ).
fof(t4_binop_2,axiom,
k3_binop_1(k4_numbers,k44_binop_2) = np__0 ).
fof(t5_binop_2,axiom,
k3_binop_1(k5_numbers,k47_binop_2) = np__0 ).
fof(t6_binop_2,axiom,
k3_binop_1(k2_numbers,k29_binop_2) = np__1 ).
fof(t7_binop_2,axiom,
k3_binop_1(k1_numbers,k35_binop_2) = np__1 ).
fof(t8_binop_2,axiom,
k3_binop_1(k3_numbers,k41_binop_2) = np__1 ).
fof(t9_binop_2,axiom,
k3_binop_1(k4_numbers,k46_binop_2) = np__1 ).
fof(t10_binop_2,axiom,
k3_binop_1(k5_numbers,k48_binop_2) = np__1 ).
fof(s1_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,f1_s1_binop_2,f2_s1_binop_2)
& m2_relset_1(A,f1_s1_binop_2,f2_s1_binop_2) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,f1_s1_binop_2,f2_s1_binop_2)
& m2_relset_1(B,f1_s1_binop_2,f2_s1_binop_2) )
=> ( ( ! [C] :
( m1_subset_1(C,f1_s1_binop_2)
=> k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,A,C) = f3_s1_binop_2(C) )
& ! [C] :
( m1_subset_1(C,f1_s1_binop_2)
=> k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,B,C) = f3_s1_binop_2(C) ) )
=> A = B ) ) ) ).
fof(s2_binop_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2)
& m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2)
& m2_relset_1(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) )
=> ( ( ! [C] :
( m1_subset_1(C,f1_s2_binop_2)
=> ! [D] :
( m1_subset_1(D,f1_s2_binop_2)
=> k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,A,C,D) = f2_s2_binop_2(C,D) ) )
& ! [C] :
( m1_subset_1(C,f1_s2_binop_2)
=> ! [D] :
( m1_subset_1(D,f1_s2_binop_2)
=> k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,B,C,D) = f2_s2_binop_2(C,D) ) ) )
=> A = B ) ) ) ).
fof(dt_k1_binop_2,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> m1_subset_1(k1_binop_2(A),k2_numbers) ) ).
fof(involutiveness_k1_binop_2,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k1_binop_2(k1_binop_2(A)) = A ) ).
fof(redefinition_k1_binop_2,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k1_binop_2(A) = k4_xcmplx_0(A) ) ).
fof(dt_k2_binop_2,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> m1_subset_1(k2_binop_2(A),k2_numbers) ) ).
fof(involutiveness_k2_binop_2,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k2_binop_2(k2_binop_2(A)) = A ) ).
fof(redefinition_k2_binop_2,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k2_binop_2(A) = k5_xcmplx_0(A) ) ).
fof(dt_k3_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers) )
=> m1_subset_1(k3_binop_2(A,B),k2_numbers) ) ).
fof(commutativity_k3_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers) )
=> k3_binop_2(A,B) = k3_binop_2(B,A) ) ).
fof(redefinition_k3_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers) )
=> k3_binop_2(A,B) = k2_xcmplx_0(A,B) ) ).
fof(dt_k4_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers) )
=> m1_subset_1(k4_binop_2(A,B),k2_numbers) ) ).
fof(redefinition_k4_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers) )
=> k4_binop_2(A,B) = k6_xcmplx_0(A,B) ) ).
fof(dt_k5_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers) )
=> m1_subset_1(k5_binop_2(A,B),k2_numbers) ) ).
fof(commutativity_k5_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers) )
=> k5_binop_2(A,B) = k5_binop_2(B,A) ) ).
fof(redefinition_k5_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers) )
=> k5_binop_2(A,B) = k3_xcmplx_0(A,B) ) ).
fof(dt_k6_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers) )
=> m1_subset_1(k6_binop_2(A,B),k2_numbers) ) ).
fof(redefinition_k6_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers) )
=> k6_binop_2(A,B) = k7_xcmplx_0(A,B) ) ).
fof(dt_k7_binop_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> m1_subset_1(k7_binop_2(A),k1_numbers) ) ).
fof(involutiveness_k7_binop_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> k7_binop_2(k7_binop_2(A)) = A ) ).
fof(redefinition_k7_binop_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> k7_binop_2(A) = k4_xcmplx_0(A) ) ).
fof(dt_k8_binop_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> m1_subset_1(k8_binop_2(A),k1_numbers) ) ).
fof(involutiveness_k8_binop_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> k8_binop_2(k8_binop_2(A)) = A ) ).
fof(redefinition_k8_binop_2,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> k8_binop_2(A) = k5_xcmplx_0(A) ) ).
fof(dt_k9_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> m1_subset_1(k9_binop_2(A,B),k1_numbers) ) ).
fof(commutativity_k9_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> k9_binop_2(A,B) = k9_binop_2(B,A) ) ).
fof(redefinition_k9_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> k9_binop_2(A,B) = k2_xcmplx_0(A,B) ) ).
fof(dt_k10_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> m1_subset_1(k10_binop_2(A,B),k1_numbers) ) ).
fof(redefinition_k10_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> k10_binop_2(A,B) = k6_xcmplx_0(A,B) ) ).
fof(dt_k11_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> m1_subset_1(k11_binop_2(A,B),k1_numbers) ) ).
fof(commutativity_k11_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> k11_binop_2(A,B) = k11_binop_2(B,A) ) ).
fof(redefinition_k11_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> k11_binop_2(A,B) = k3_xcmplx_0(A,B) ) ).
fof(dt_k12_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> m1_subset_1(k12_binop_2(A,B),k1_numbers) ) ).
fof(redefinition_k12_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> k12_binop_2(A,B) = k7_xcmplx_0(A,B) ) ).
fof(dt_k13_binop_2,axiom,
! [A] :
( m1_subset_1(A,k3_numbers)
=> m1_subset_1(k13_binop_2(A),k3_numbers) ) ).
fof(involutiveness_k13_binop_2,axiom,
! [A] :
( m1_subset_1(A,k3_numbers)
=> k13_binop_2(k13_binop_2(A)) = A ) ).
fof(redefinition_k13_binop_2,axiom,
! [A] :
( m1_subset_1(A,k3_numbers)
=> k13_binop_2(A) = k4_xcmplx_0(A) ) ).
fof(dt_k14_binop_2,axiom,
! [A] :
( m1_subset_1(A,k3_numbers)
=> m1_subset_1(k14_binop_2(A),k3_numbers) ) ).
fof(involutiveness_k14_binop_2,axiom,
! [A] :
( m1_subset_1(A,k3_numbers)
=> k14_binop_2(k14_binop_2(A)) = A ) ).
fof(redefinition_k14_binop_2,axiom,
! [A] :
( m1_subset_1(A,k3_numbers)
=> k14_binop_2(A) = k5_xcmplx_0(A) ) ).
fof(dt_k15_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_numbers)
& m1_subset_1(B,k3_numbers) )
=> m1_subset_1(k15_binop_2(A,B),k3_numbers) ) ).
fof(commutativity_k15_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_numbers)
& m1_subset_1(B,k3_numbers) )
=> k15_binop_2(A,B) = k15_binop_2(B,A) ) ).
fof(redefinition_k15_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_numbers)
& m1_subset_1(B,k3_numbers) )
=> k15_binop_2(A,B) = k2_xcmplx_0(A,B) ) ).
fof(dt_k16_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_numbers)
& m1_subset_1(B,k3_numbers) )
=> m1_subset_1(k16_binop_2(A,B),k3_numbers) ) ).
fof(redefinition_k16_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_numbers)
& m1_subset_1(B,k3_numbers) )
=> k16_binop_2(A,B) = k6_xcmplx_0(A,B) ) ).
fof(dt_k17_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_numbers)
& m1_subset_1(B,k3_numbers) )
=> m1_subset_1(k17_binop_2(A,B),k3_numbers) ) ).
fof(commutativity_k17_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_numbers)
& m1_subset_1(B,k3_numbers) )
=> k17_binop_2(A,B) = k17_binop_2(B,A) ) ).
fof(redefinition_k17_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_numbers)
& m1_subset_1(B,k3_numbers) )
=> k17_binop_2(A,B) = k3_xcmplx_0(A,B) ) ).
fof(dt_k18_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_numbers)
& m1_subset_1(B,k3_numbers) )
=> m1_subset_1(k18_binop_2(A,B),k3_numbers) ) ).
fof(redefinition_k18_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k3_numbers)
& m1_subset_1(B,k3_numbers) )
=> k18_binop_2(A,B) = k7_xcmplx_0(A,B) ) ).
fof(dt_k19_binop_2,axiom,
! [A] :
( m1_subset_1(A,k4_numbers)
=> m1_subset_1(k19_binop_2(A),k4_numbers) ) ).
fof(involutiveness_k19_binop_2,axiom,
! [A] :
( m1_subset_1(A,k4_numbers)
=> k19_binop_2(k19_binop_2(A)) = A ) ).
fof(redefinition_k19_binop_2,axiom,
! [A] :
( m1_subset_1(A,k4_numbers)
=> k19_binop_2(A) = k4_xcmplx_0(A) ) ).
fof(dt_k20_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_numbers)
& m1_subset_1(B,k4_numbers) )
=> m1_subset_1(k20_binop_2(A,B),k4_numbers) ) ).
fof(commutativity_k20_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_numbers)
& m1_subset_1(B,k4_numbers) )
=> k20_binop_2(A,B) = k20_binop_2(B,A) ) ).
fof(redefinition_k20_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_numbers)
& m1_subset_1(B,k4_numbers) )
=> k20_binop_2(A,B) = k2_xcmplx_0(A,B) ) ).
fof(dt_k21_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_numbers)
& m1_subset_1(B,k4_numbers) )
=> m1_subset_1(k21_binop_2(A,B),k4_numbers) ) ).
fof(redefinition_k21_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_numbers)
& m1_subset_1(B,k4_numbers) )
=> k21_binop_2(A,B) = k6_xcmplx_0(A,B) ) ).
fof(dt_k22_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_numbers)
& m1_subset_1(B,k4_numbers) )
=> m1_subset_1(k22_binop_2(A,B),k4_numbers) ) ).
fof(commutativity_k22_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_numbers)
& m1_subset_1(B,k4_numbers) )
=> k22_binop_2(A,B) = k22_binop_2(B,A) ) ).
fof(redefinition_k22_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_numbers)
& m1_subset_1(B,k4_numbers) )
=> k22_binop_2(A,B) = k3_xcmplx_0(A,B) ) ).
fof(dt_k23_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers) ) ).
fof(commutativity_k23_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> k23_binop_2(A,B) = k23_binop_2(B,A) ) ).
fof(redefinition_k23_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> k23_binop_2(A,B) = k2_xcmplx_0(A,B) ) ).
fof(dt_k24_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k24_binop_2(A,B),k1_numbers,k5_numbers) ) ).
fof(commutativity_k24_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> k24_binop_2(A,B) = k24_binop_2(B,A) ) ).
fof(redefinition_k24_binop_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> k24_binop_2(A,B) = k3_xcmplx_0(A,B) ) ).
fof(dt_k25_binop_2,axiom,
( v1_funct_1(k25_binop_2)
& v1_funct_2(k25_binop_2,k2_numbers,k2_numbers)
& m2_relset_1(k25_binop_2,k2_numbers,k2_numbers) ) ).
fof(dt_k26_binop_2,axiom,
( v1_funct_1(k26_binop_2)
& v1_funct_2(k26_binop_2,k2_numbers,k2_numbers)
& m2_relset_1(k26_binop_2,k2_numbers,k2_numbers) ) ).
fof(dt_k27_binop_2,axiom,
( v1_funct_1(k27_binop_2)
& v1_funct_2(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& m2_relset_1(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) ) ).
fof(dt_k28_binop_2,axiom,
( v1_funct_1(k28_binop_2)
& v1_funct_2(k28_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& m2_relset_1(k28_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) ) ).
fof(dt_k29_binop_2,axiom,
( v1_funct_1(k29_binop_2)
& v1_funct_2(k29_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& m2_relset_1(k29_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) ) ).
fof(dt_k30_binop_2,axiom,
( v1_funct_1(k30_binop_2)
& v1_funct_2(k30_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
& m2_relset_1(k30_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) ) ).
fof(dt_k31_binop_2,axiom,
( v1_funct_1(k31_binop_2)
& v1_funct_2(k31_binop_2,k1_numbers,k1_numbers)
& m2_relset_1(k31_binop_2,k1_numbers,k1_numbers) ) ).
fof(dt_k32_binop_2,axiom,
( v1_funct_1(k32_binop_2)
& v1_funct_2(k32_binop_2,k1_numbers,k1_numbers)
& m2_relset_1(k32_binop_2,k1_numbers,k1_numbers) ) ).
fof(dt_k33_binop_2,axiom,
( v1_funct_1(k33_binop_2)
& v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ) ).
fof(dt_k34_binop_2,axiom,
( v1_funct_1(k34_binop_2)
& v1_funct_2(k34_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(k34_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ) ).
fof(dt_k35_binop_2,axiom,
( v1_funct_1(k35_binop_2)
& v1_funct_2(k35_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(k35_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ) ).
fof(dt_k36_binop_2,axiom,
( v1_funct_1(k36_binop_2)
& v1_funct_2(k36_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(k36_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ) ).
fof(dt_k37_binop_2,axiom,
( v1_funct_1(k37_binop_2)
& v1_funct_2(k37_binop_2,k3_numbers,k3_numbers)
& m2_relset_1(k37_binop_2,k3_numbers,k3_numbers) ) ).
fof(dt_k38_binop_2,axiom,
( v1_funct_1(k38_binop_2)
& v1_funct_2(k38_binop_2,k3_numbers,k3_numbers)
& m2_relset_1(k38_binop_2,k3_numbers,k3_numbers) ) ).
fof(dt_k39_binop_2,axiom,
( v1_funct_1(k39_binop_2)
& v1_funct_2(k39_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& m2_relset_1(k39_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) ) ).
fof(dt_k40_binop_2,axiom,
( v1_funct_1(k40_binop_2)
& v1_funct_2(k40_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& m2_relset_1(k40_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) ) ).
fof(dt_k41_binop_2,axiom,
( v1_funct_1(k41_binop_2)
& v1_funct_2(k41_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& m2_relset_1(k41_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) ) ).
fof(dt_k42_binop_2,axiom,
( v1_funct_1(k42_binop_2)
& v1_funct_2(k42_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
& m2_relset_1(k42_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) ) ).
fof(dt_k43_binop_2,axiom,
( v1_funct_1(k43_binop_2)
& v1_funct_2(k43_binop_2,k4_numbers,k4_numbers)
& m2_relset_1(k43_binop_2,k4_numbers,k4_numbers) ) ).
fof(dt_k44_binop_2,axiom,
( v1_funct_1(k44_binop_2)
& v1_funct_2(k44_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
& m2_relset_1(k44_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) ) ).
fof(dt_k45_binop_2,axiom,
( v1_funct_1(k45_binop_2)
& v1_funct_2(k45_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
& m2_relset_1(k45_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) ) ).
fof(dt_k46_binop_2,axiom,
( v1_funct_1(k46_binop_2)
& v1_funct_2(k46_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
& m2_relset_1(k46_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) ) ).
fof(dt_k47_binop_2,axiom,
( v1_funct_1(k47_binop_2)
& v1_funct_2(k47_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& m2_relset_1(k47_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) ) ).
fof(dt_k48_binop_2,axiom,
( v1_funct_1(k48_binop_2)
& v1_funct_2(k48_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
& m2_relset_1(k48_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) ) ).
%------------------------------------------------------------------------------