% Mizar problem: e13_2_1,zf_model,529,23 
include('Axioms/SET010^0.ax').
thf(c1_2_1_type,type,( c1_2_1__zf_model: $i )).
thf(c2_2_1_type,type,( c2_2_1__zf_model: $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k20_zf_lang_type,type,( k20_zf_lang: $i > $i )).
thf(k21_zf_lang_type,type,( k21_zf_lang: $i > $i )).
thf(k22_zf_lang_type,type,( k22_zf_lang: $i > $i )).
thf(k24_zf_lang_type,type,( k24_zf_lang: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(m1_finseq_1_type,type,( m1_finseq_1: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_finseq_1_type,type,( m2_finseq_1: $i > $i > $o )).
thf(v1_finseq_1_type,type,( v1_finseq_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_subset_1_type,type,( v1_subset_1: $i > $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_zf_lang_type,type,( v1_zf_lang: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_zf_lang_type,type,( v4_zf_lang: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_zf_lang_type,type,( v5_zf_lang: $i > $o )).
thf(v6_zf_lang_type,type,( v6_zf_lang: $i > $o )).
thf(v7_zf_lang_type,type,( v7_zf_lang: $i > $o )).
thf(cc2_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ~ ( v1_subset_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ) ),file(subset_1,cc2_subset_1)).
thf(rc3_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_subset_1 @ B @ A ) ) ),file(subset_1,rc3_subset_1)).
thf(rc4_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,rc4_subset_1)).
thf(cc1_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_xboole_0 @ B ) ) ) ),file(subset_1,cc1_subset_1)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc3_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ( v1_xboole_0 @ B ) => ( v1_subset_1 @ B @ A ) ) ) ) ),file(subset_1,cc3_subset_1)).
thf(cc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc4_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ~ ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,cc4_subset_1)).
thf(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(rc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relset_1,rc1_relset_1)).
thf(rc1_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(subset_1,rc1_subset_1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_xboole_0 @ B ) ) ),file(subset_1,rc2_subset_1)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_m1_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_finseq_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) ) ),file(finseq_1,m1_finseq_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_m2_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m2_finseq_1 @ B @ A ) <=> ( m1_finseq_1 @ B @ A ) ) ),file(finseq_1,m2_finseq_1)).
thf(dt_k20_zf_lang,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m1_finseq_1 @ A @ k5_numbers ) ) => ( ( v1_zf_lang @ ( k20_zf_lang @ A ) ) & ( m2_finseq_1 @ ( k20_zf_lang @ A ) @ k5_numbers ) ) ) ),file(zf_lang,k20_zf_lang)).
thf(dt_k21_zf_lang,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m1_finseq_1 @ A @ k5_numbers ) ) => ( ( v1_zf_lang @ ( k21_zf_lang @ A ) ) & ( m2_finseq_1 @ ( k21_zf_lang @ A ) @ k5_numbers ) ) ) ),file(zf_lang,k21_zf_lang)).
thf(dt_k22_zf_lang,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m1_finseq_1 @ A @ k5_numbers ) ) => ( ( v1_zf_lang @ ( k22_zf_lang @ A ) ) & ( m2_finseq_1 @ ( k22_zf_lang @ A ) @ k5_numbers ) ) ) ),file(zf_lang,k22_zf_lang)).
thf(dt_k24_zf_lang,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m1_finseq_1 @ A @ k5_numbers ) ) => ( ( v1_zf_lang @ ( k24_zf_lang @ A ) ) & ( m2_finseq_1 @ ( k24_zf_lang @ A ) @ k5_numbers ) ) ) ),file(zf_lang,k24_zf_lang)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_m2_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m2_finseq_1 @ B @ A ) => ( ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) ) ) ),file(finseq_1,m2_finseq_1)).
thf(dt_c1_2_1__zf_model,axiom,( $true ),file(zf_model,c1_2_1__zf_model)).
thf(dt_c2_2_1__zf_model,axiom,( $true ),file(zf_model,c2_2_1__zf_model)).
thf(e10_2_1__zf_model,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m2_finseq_1 @ A @ k5_numbers ) ) => ( ( v7_zf_lang @ A ) => ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ c1_2_1__zf_model ) & ( r2_hidden @ ( k4_tarski @ A @ C ) @ c2_2_1__zf_model ) ) => ( = @ B @ C ) ) ) ) ),file(zf_model,e10_2_1__zf_model)).
thf(e12_2_1__zf_model,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m2_finseq_1 @ A @ k5_numbers ) ) => ( ( ( v4_zf_lang @ A ) & ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ ( k4_tarski @ ( k20_zf_lang @ A ) @ B ) @ c1_2_1__zf_model ) & ( r2_hidden @ ( k4_tarski @ ( k20_zf_lang @ A ) @ C ) @ c2_2_1__zf_model ) ) => ( = @ B @ C ) ) ) => ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ c1_2_1__zf_model ) & ( r2_hidden @ ( k4_tarski @ A @ C ) @ c2_2_1__zf_model ) ) => ( = @ B @ C ) ) ) ) ),file(zf_model,e12_2_1__zf_model)).
thf(e11_2_1__zf_model,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m2_finseq_1 @ A @ k5_numbers ) ) => ( ( ( v5_zf_lang @ A ) & ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ ( k4_tarski @ ( k21_zf_lang @ A ) @ B ) @ c1_2_1__zf_model ) & ( r2_hidden @ ( k4_tarski @ ( k21_zf_lang @ A ) @ C ) @ c2_2_1__zf_model ) ) => ( = @ B @ C ) ) & ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ ( k4_tarski @ ( k22_zf_lang @ A ) @ B ) @ c1_2_1__zf_model ) & ( r2_hidden @ ( k4_tarski @ ( k22_zf_lang @ A ) @ C ) @ c2_2_1__zf_model ) ) => ( = @ B @ C ) ) ) => ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ c1_2_1__zf_model ) & ( r2_hidden @ ( k4_tarski @ A @ C ) @ c2_2_1__zf_model ) ) => ( = @ B @ C ) ) ) ) ),file(zf_model,e11_2_1__zf_model)).
thf(e9_2_1__zf_model,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m2_finseq_1 @ A @ k5_numbers ) ) => ( ( ( v6_zf_lang @ A ) & ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ ( k4_tarski @ ( k24_zf_lang @ A ) @ B ) @ c1_2_1__zf_model ) & ( r2_hidden @ ( k4_tarski @ ( k24_zf_lang @ A ) @ C ) @ c2_2_1__zf_model ) ) => ( = @ B @ C ) ) ) => ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ c1_2_1__zf_model ) & ( r2_hidden @ ( k4_tarski @ A @ C ) @ c2_2_1__zf_model ) ) => ( = @ B @ C ) ) ) ) ),file(zf_model,e9_2_1__zf_model)).
thf(s1_zf_lang,axiom,( ! [A: $i > $o] : ( ( ! [B: $i] : ( ( ( v1_zf_lang @ B ) & ( m2_finseq_1 @ B @ k5_numbers ) ) => ( ( v7_zf_lang @ B ) => ( A @ B ) ) ) & ! [B: $i] : ( ( ( v1_zf_lang @ B ) & ( m2_finseq_1 @ B @ k5_numbers ) ) => ( ( ( v4_zf_lang @ B ) & ( A @ ( k20_zf_lang @ B ) ) ) => ( A @ B ) ) ) & ! [B: $i] : ( ( ( v1_zf_lang @ B ) & ( m2_finseq_1 @ B @ k5_numbers ) ) => ( ( ( v5_zf_lang @ B ) & ( A @ ( k21_zf_lang @ B ) ) & ( A @ ( k22_zf_lang @ B ) ) ) => ( A @ B ) ) ) & ! [B: $i] : ( ( ( v1_zf_lang @ B ) & ( m2_finseq_1 @ B @ k5_numbers ) ) => ( ( ( v6_zf_lang @ B ) & ( A @ ( k24_zf_lang @ B ) ) ) => ( A @ B ) ) ) ) => ! [B: $i] : ( ( ( v1_zf_lang @ B ) & ( m2_finseq_1 @ B @ k5_numbers ) ) => ( A @ B ) ) ) ),file(zf_lang,s1_zf_lang)).
thf(e13_2_1__zf_model,conjecture,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m2_finseq_1 @ A @ k5_numbers ) ) => ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ c1_2_1__zf_model ) & ( r2_hidden @ ( k4_tarski @ A @ C ) @ c2_2_1__zf_model ) ) => ( = @ B @ C ) ) ) ),file(zf_model,e13_2_1__zf_model)).
