include('Axioms/SET010^0.ax').
thf(v1_relat_1_type, type, v1_relat_1: $i > $o).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v1_funct_2_type, type, v1_funct_2: $i > $i > $i > $o).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k4_partfun1_type, type, k4_partfun1: $i > $i > $i).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i).
thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i).
thf(m2_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(t2_subset, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_hidden @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(t1_subset, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(redefinition_m2_subset_1, axiom,   (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ A)  @ B)  <=>  ( (m1_subset_1 @ C)  @ B) ) ) ) ) , file(subset_1, m2_subset_1)).
thf(redefinition_k5_numbers, axiom,   ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(l1_seqfunc, axiom,   (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @  ( (k4_partfun1 @ A)  @ B) )  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  ( (k4_partfun1 @ A)  @ B) ) ) ) ) )  <=>  ( ( (= @  (k9_xtuple_0 @ C) )  @ k5_numbers)  &  (! [D: $i] :  ( ( (r2_hidden @ D)  @ k5_numbers)  =>  ( (v1_funct_1 @  ( (k1_funct_1 @ C)  @ D) )  &  ( (m1_subset_1 @  ( (k1_funct_1 @ C)  @ D) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) , file(seqfunc, l1_seqfunc)).
thf(fc6_ordinal1, axiom,   ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc1_numbers, axiom,   ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers)).
thf(dt_k5_numbers, axiom,   ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(t1_seqfunc, conjecture,   (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @  ( (k4_partfun1 @ A)  @ B) )  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  ( (k4_partfun1 @ A)  @ B) ) ) ) ) )  <=>  ( ( (= @  (k9_xtuple_0 @ C) )  @ k5_numbers)  &  (! [D: $i] :  ( ( ( (m2_subset_1 @ D)  @ k1_numbers)  @ k5_numbers)  =>  ( (v1_funct_1 @  ( (k1_funct_1 @ C)  @ D) )  &  ( (m1_subset_1 @  ( (k1_funct_1 @ C)  @ D) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) , file(seqfunc, t1_seqfunc)).