% Mizar problem: s1_ordinal4,ordinal4,1731,16 
include('Axioms/SET010^0.ax').
thf(k5_relat_1_type,type,( k5_relat_1: $i > $i > $i )).
thf(n0_type,type,( np__0: $i )).
thf(n1_type,type,( np__1: $i )).
thf(f1_s1_ordinal4_type,type,( f1_s1_ordinal4: $i > $i )).
thf(k10_ordinal2_type,type,( k10_ordinal2: $i > $i > $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_ordinal1_type,type,( k1_ordinal1: $i > $i )).
thf(k1_tarski_type,type,( k1_tarski: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k3_ordinal2_type,type,( k3_ordinal2: $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_ordinal2_type,type,( k4_ordinal2: $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k8_ordinal2_type,type,( k8_ordinal2: $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_ordinal2_type,type,( r1_ordinal2: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r2_xboole_0_type,type,( r2_xboole_0: $i > $i > $o )).
thf(v1_card_1_type,type,( v1_card_1: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_ordinal2_type,type,( v1_ordinal2: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_card_1_type,type,( v2_card_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_ordinal2_type,type,( v2_ordinal2: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_card_1_type,type,( v3_card_1: $i > $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_ordinal1_type,type,( v4_ordinal1: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(antisymmetry_r2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_xboole_0 @ A @ B ) => ~ ( r2_xboole_0 @ B @ A ) ) ),file(xboole_0,r2_xboole_0)).
thf(cc10_card_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) => ( v3_card_1 @ A @ np__1 ) ) ),file(card_1,cc10_card_1)).
thf(cc10_ordinal1,axiom,( ! [A: $i] : ( ( v6_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_ordinal1 @ B ) ) ) ),file(ordinal1,cc10_ordinal1)).
thf(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc2_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc2_card_1)).
thf(cc2_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ) ),file(funct_1,cc2_funct_1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal2,cc2_ordinal2)).
thf(cc3_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc3_card_1)).
thf(cc3_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_funct_1 @ B ) ) ) ),file(funct_1,cc3_funct_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc4_card_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc4_card_1)).
thf(cc4_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc4_funct_1)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc5_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc5_card_1)).
thf(cc5_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ) ),file(funct_1,cc5_funct_1)).
thf(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(cc6_card_1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) ) => ( v7_ordinal1 @ A ) ) ),file(card_1,cc6_card_1)).
thf(cc6_funct_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc6_funct_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc7_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ k1_xboole_0 ) => ( v1_xboole_0 @ A ) ) ),file(card_1,cc7_card_1)).
thf(cc7_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc8_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_card_1 @ A @ k1_xboole_0 ) ) ),file(card_1,cc8_card_1)).
thf(cc8_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) ) ) ),file(funct_1,cc8_funct_1)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(cc9_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ np__1 ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) ) ),file(card_1,cc9_card_1)).
thf(cc9_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_funct_1 @ B ) ) ) ),file(funct_1,cc9_funct_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(commutativity_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ A ) ) ),file(xboole_0,k2_xboole_0)).
thf(connectedness_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) | ( r1_ordinal1 @ B @ A ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(d10_ordinal2,axiom,( ! [A: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) => ( ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( r1_ordinal2 @ B @ A ) ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( = @ B @ ( k8_ordinal2 @ A ) ) <=> ( r1_ordinal2 @ B @ A ) ) ) ) ) ),file(ordinal2,d10_ordinal2)).
thf(d11_ordinal1,axiom,( ! [A: $i] : ( ( = @ A @ k4_ordinal1 ) <=> ( ( r2_hidden @ k1_xboole_0 @ A ) & ( v4_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( ( r2_hidden @ k1_xboole_0 @ B ) & ( v4_ordinal1 @ B ) ) => ( r1_tarski @ A @ B ) ) ) ) ) ),file(ordinal1,d11_ordinal1)).
thf(d12_ordinal2,axiom,( ! [A: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) => ( ( v2_ordinal2 @ A ) <=> ! [B: $i] : ( ( v3_ordinal1 @ B ) => ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( ( r2_hidden @ B @ C ) & ( r2_hidden @ C @ ( k9_xtuple_0 @ A ) ) ) => ( r2_hidden @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ A @ C ) ) ) ) ) ) ) ),file(ordinal2,d12_ordinal2)).
thf(d1_ordinal1,axiom,( ! [A: $i] : ( = @ ( k1_ordinal1 @ A ) @ ( k2_xboole_0 @ A @ ( k1_tarski @ A ) ) ) ),file(ordinal1,d1_ordinal1)).
thf(d2_ordinal1,axiom,( ! [A: $i] : ( ( v1_ordinal1 @ A ) <=> ! [B: $i] : ( ( r2_hidden @ B @ A ) => ( r1_tarski @ B @ A ) ) ) ),file(ordinal1,d2_ordinal1)).
thf(d2_xboole_0,axiom,( = @ k1_xboole_0 @ ( eps @ ^ [A: $i] : ( v1_xboole_0 @ A ) ) ),file(xboole_0,d2_xboole_0)).
thf(d3_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( = @ B @ ( k10_xtuple_0 @ A ) ) <=> ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ? [D: $i] : ( ( r2_hidden @ D @ ( k9_xtuple_0 @ A ) ) & ( = @ C @ ( k1_funct_1 @ A @ D ) ) ) ) ) ) ),file(funct_1,d3_funct_1)).
thf(d3_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( ( r1_tarski @ A @ B ) <=> ! [C: $i] : ( ( r2_hidden @ C @ A ) => ( r2_hidden @ C @ B ) ) ) ),file(tarski,d3_tarski)).
thf(d5_ordinal2,axiom,( ! [A: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( = @ ( k4_ordinal2 @ A ) @ ( k3_ordinal2 @ ( k10_xtuple_0 @ A ) ) ) ) ),file(ordinal2,d5_ordinal2)).
thf(d8_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_xboole_0 @ A @ B ) <=> ( ( r1_tarski @ A @ B ) & ~ ( = @ A @ B ) ) ) ),file(xboole_0,d8_xboole_0)).
thf(dt_f1_s1_ordinal4,axiom,( ! [A: $i] : ( v3_ordinal1 @ ( f1_s1_ordinal4 @ A ) ) ),file(ordinal4,f1_s1_ordinal4)).
thf(dt_k10_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k10_ordinal2 @ A @ B ) ) ) ),file(ordinal2,k10_ordinal2)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_ordinal1,axiom,( $true ),file(ordinal1,k1_ordinal1)).
thf(dt_k1_tarski,axiom,( $true ),file(tarski,k1_tarski)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
thf(dt_k3_ordinal2,axiom,( ! [A: $i] : ( v3_ordinal1 @ ( k3_ordinal2 @ A ) ) ),file(ordinal2,k3_ordinal2)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k4_ordinal2,axiom,( ! [A: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v3_ordinal1 @ ( k4_ordinal2 @ A ) ) ) ),file(ordinal2,k4_ordinal2)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k8_ordinal2,axiom,( ! [A: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) => ( v3_ordinal1 @ ( k8_ordinal2 @ A ) ) ) ),file(ordinal2,k8_ordinal2)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_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 @ A ) ) ) ),file(subset_1,m2_subset_1)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(existence_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 ) ) ),file(subset_1,m2_subset_1)).
thf(fc12_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) => ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc12_funct_1)).
thf(fc13_card_1,axiom,( ! [A: $i] : ( v3_card_1 @ ( k1_tarski @ A ) @ np__1 ) ),file(card_1,fc13_card_1)).
thf(fc13_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc13_funct_1)).
thf(fc14_card_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_card_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v3_card_1 @ B @ A ) ) => ( v3_card_1 @ ( k9_xtuple_0 @ B ) @ A ) ) ),file(card_1,fc14_card_1)).
thf(fc14_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v4_funct_1 @ ( k1_tarski @ A ) ) ) ),file(funct_1,fc14_funct_1)).
thf(fc18_funct_1,axiom,( ! [A: $i] : ( ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(funct_1,fc18_funct_1)).
thf(fc1_ordinal1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_ordinal1 @ A ) ) ),file(ordinal1,fc1_ordinal1)).
thf(fc1_ordinal3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(ordinal3,fc1_ordinal3)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc2_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ~ ( v1_xboole_0 @ ( k1_ordinal1 @ A ) ) & ( v3_ordinal1 @ ( k1_ordinal1 @ A ) ) ) ) ),file(ordinal1,fc2_ordinal1)).
thf(fc2_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(ordinal2,fc2_ordinal2)).
thf(fc2_xboole_0,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ) ),file(xboole_0,fc2_xboole_0)).
thf(fc4_card_1,axiom,( v1_card_1 @ k4_ordinal1 ),file(card_1,fc4_card_1)).
thf(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
thf(fc4_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ A ) => ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(xboole_0,fc4_xboole_0)).
thf(fc5_card_1,axiom,( v2_card_1 @ k4_ordinal1 ),file(card_1,fc5_card_1)).
thf(fc5_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( ( v3_ordinal1 @ ( k10_ordinal2 @ A @ B ) ) & ( v7_ordinal1 @ ( k10_ordinal2 @ A @ B ) ) ) ) ),file(ordinal2,fc5_ordinal2)).
thf(fc5_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ A ) => ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ) ),file(xboole_0,fc5_xboole_0)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(fc7_card_1,axiom,( ~ ( v1_finset_1 @ k4_ordinal1 ) ),file(card_1,fc7_card_1)).
thf(fc7_ordinal1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) => ( v7_ordinal1 @ ( k1_ordinal1 @ A ) ) ) ),file(ordinal1,fc7_ordinal1)).
thf(fc9_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(card_1,fc9_card_1)).
thf(idempotence_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k2_xboole_0)).
thf(irreflexivity_r2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ~ ( r2_xboole_0 @ A @ A ) ),file(xboole_0,r2_xboole_0)).
thf(l1_ordinal4,axiom,( r2_hidden @ k1_xboole_0 @ k4_ordinal1 ),file(ordinal4,l1_ordinal4)).
thf(l2_ordinal4,axiom,( v4_ordinal1 @ k4_ordinal1 ),file(ordinal4,l2_ordinal4)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_ordinal2,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v4_ordinal1 @ A ) ) ),file(ordinal2,rc1_ordinal2)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_card_1,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(card_1,rc2_card_1)).
thf(rc2_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ),file(funct_1,rc2_funct_1)).
thf(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(rc2_ordinal2,axiom,( ? [A: $i] : ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) ),file(ordinal2,rc2_ordinal2)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc3_card_1,axiom,( ? [A: $i] : ~ ( v1_finset_1 @ A ) ),file(card_1,rc3_card_1)).
thf(rc4_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_finset_1 @ B ) ) ) ),file(card_1,rc4_card_1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc5_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( v3_card_1 @ B @ A ) ) ),file(card_1,rc5_card_1)).
thf(rc5_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) ),file(funct_1,rc5_funct_1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(rc6_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v3_card_1 @ B @ A ) ) ) ),file(card_1,rc6_card_1)).
thf(rc7_card_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v3_card_1 @ B @ np__1 ) ) ) ),file(card_1,rc7_card_1)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
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_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) <=> ( r1_tarski @ A @ B ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(reflexivity_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( r1_ordinal1 @ A @ A ) ) ),file(ordinal1,r1_ordinal1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(rqSucc__k1_ordinal1__r0_r1,axiom,( = @ ( k1_ordinal1 @ np__0 ) @ np__1 ),file(arithm,rqSucc__k1_ordinal1__r0_r1)).
thf(spc0_boole,axiom,( v1_xboole_0 @ np__0 ),file(boole,spc0_boole)).
thf(spc0_numerals,axiom,( ( m2_subset_1 @ np__0 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__0 @ k5_numbers ) & ( m1_subset_1 @ np__0 @ k1_numbers ) ),file(numerals,spc0_numerals)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(spc1_numerals,axiom,( ( v2_xxreal_0 @ np__1 ) & ( m2_subset_1 @ np__1 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k1_numbers ) ),file(numerals,spc1_numerals)).
thf(t10_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( v1_ordinal1 @ C ) => ( ( ( r2_hidden @ A @ B ) & ( r2_hidden @ B @ C ) ) => ( r2_hidden @ A @ C ) ) ) ),file(ordinal1,t10_ordinal1)).
thf(t11_ordinal1,axiom,( ! [A: $i] : ( ( v1_ordinal1 @ A ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_xboole_0 @ A @ B ) => ( r2_hidden @ A @ B ) ) ) ) ),file(ordinal1,t11_ordinal1)).
thf(t12_ordinal1,axiom,( ! [A: $i] : ( ( v1_ordinal1 @ A ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( ( r1_tarski @ A @ B ) & ( r2_hidden @ B @ C ) ) => ( r2_hidden @ A @ C ) ) ) ) ) ),file(ordinal1,t12_ordinal1)).
thf(t16_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r1_ordinal1 @ A @ B ) | ( r2_hidden @ B @ A ) ) ) ) ),file(ordinal1,t16_ordinal1)).
thf(t16_ordinal4,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) => ( ( ( v2_ordinal2 @ A ) & ( v4_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) => ( v4_ordinal1 @ ( k4_ordinal2 @ A ) ) ) ) ),file(ordinal4,t16_ordinal4)).
thf(t19_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( r2_hidden @ A @ ( k3_ordinal2 @ B ) ) ) ) ),file(ordinal2,t19_ordinal2)).
thf(t1_boole,axiom,( ! [A: $i] : ( = @ ( k2_xboole_0 @ A @ k1_xboole_0 ) @ A ) ),file(boole,t1_boole)).
thf(t1_numerals,axiom,( m1_subset_1 @ k1_xboole_0 @ k4_ordinal1 ),file(numerals,t1_numerals)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t21_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ~ ( ( r2_hidden @ A @ ( k3_ordinal2 @ B ) ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ~ ( ( r2_hidden @ C @ B ) & ( r1_ordinal1 @ A @ C ) ) ) ) ) ),file(ordinal2,t21_ordinal2)).
thf(t26_ordinal3,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( = @ ( k10_ordinal2 @ A @ B ) @ k1_xboole_0 ) => ( ( = @ A @ k1_xboole_0 ) & ( = @ B @ k1_xboole_0 ) ) ) ) ) ),file(ordinal3,t26_ordinal3)).
thf(t27_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( = @ ( k10_ordinal2 @ A @ k1_xboole_0 ) @ A ) ) ),file(ordinal2,t27_ordinal2)).
thf(t28_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v4_ordinal1 @ A ) <=> ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ A ) => ( r2_hidden @ ( k1_ordinal1 @ B ) @ A ) ) ) ) ) ),file(ordinal1,t28_ordinal1)).
thf(t28_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( = @ ( k10_ordinal2 @ A @ ( k1_ordinal1 @ B ) ) @ ( k1_ordinal1 @ ( k10_ordinal2 @ A @ B ) ) ) ) ) ),file(ordinal2,t28_ordinal2)).
thf(t28_ordinal3,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ~ ( ( r2_hidden @ A @ B ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ~ ( ( = @ B @ ( k10_ordinal2 @ A @ C ) ) & ~ ( = @ C @ k1_xboole_0 ) ) ) ) ) ) ),file(ordinal3,t28_ordinal3)).
thf(t29_ordinal3,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( v4_ordinal1 @ A ) => ( ( = @ A @ k1_xboole_0 ) | ( v4_ordinal1 @ ( k10_ordinal2 @ B @ A ) ) ) ) ) ) ),file(ordinal3,t29_ordinal3)).
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(t3_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) <=> ( r1_tarski @ A @ B ) ) ),file(subset,t3_subset)).
thf(t4_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) ) => ( m1_subset_1 @ A @ C ) ) ),file(subset,t4_subset)).
thf(t5_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( r1_tarski @ B @ A ) ) ),file(ordinal1,t5_ordinal1)).
thf(t5_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ~ ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) & ( v1_xboole_0 @ C ) ) ),file(subset,t5_subset)).
thf(t6_boole,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( = @ A @ k1_xboole_0 ) ) ),file(boole,t6_boole)).
thf(t6_ordinal1,axiom,( ! [A: $i] : ( r2_hidden @ A @ ( k1_ordinal1 @ A ) ) ),file(ordinal1,t6_ordinal1)).
thf(t7_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t7_boole)).
thf(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
thf(t8_ordinal3,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ~ ( = @ A @ k1_xboole_0 ) => ( r2_hidden @ k1_xboole_0 @ A ) ) ) ),file(ordinal3,t8_ordinal3)).
thf(t8_ordinal4,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) => ( ( ( v4_ordinal1 @ ( k9_xtuple_0 @ A ) ) & ( v2_ordinal2 @ A ) ) => ( ( = @ ( k9_xtuple_0 @ A ) @ k1_xboole_0 ) | ( ( r1_ordinal2 @ ( k4_ordinal2 @ A ) @ A ) & ( = @ ( k8_ordinal2 @ A ) @ ( k4_ordinal2 @ A ) ) ) ) ) ) ),file(ordinal4,t8_ordinal4)).
thf(s11_ordinal2,axiom,( ! [A: $i > $i > $i] : ! [B: $i > $i > $i] : ! [C: $i] : ! [D: $i] : ? [E: $i] : ( ( v5_ordinal1 @ E ) & ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) & ( v1_ordinal2 @ E ) & ( = @ ( k9_xtuple_0 @ E ) @ D ) & ( ( r2_hidden @ k1_xboole_0 @ D ) => ( = @ ( k1_funct_1 @ E @ k1_xboole_0 ) @ C ) ) & ! [F: $i] : ( ( v3_ordinal1 @ F ) => ( ( r2_hidden @ ( k1_ordinal1 @ F ) @ D ) => ( = @ ( k1_funct_1 @ E @ ( k1_ordinal1 @ F ) ) @ ( B @ F @ ( k1_funct_1 @ E @ F ) ) ) ) ) & ! [F: $i] : ( ( v3_ordinal1 @ F ) => ( ( ( r2_hidden @ F @ D ) & ( v4_ordinal1 @ F ) ) => ( ( = @ F @ k1_xboole_0 ) | ( = @ ( k1_funct_1 @ E @ F ) @ ( A @ F @ ( k5_relat_1 @ E @ F ) ) ) ) ) ) ) ),file(ordinal2,s11_ordinal2)).
thf(s1_ordinal1,axiom,( ! [A: $i > $o] : ( ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( A @ B ) ) => ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( A @ B ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( A @ C ) => ( r1_ordinal1 @ B @ C ) ) ) ) ) ),file(ordinal1,s1_ordinal1)).
thf(s1_ordinal2,axiom,( ! [A: $i > $o] : ( ( ( A @ k1_xboole_0 ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( A @ B ) => ( A @ ( k1_ordinal1 @ B ) ) ) ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( ( v4_ordinal1 @ B ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( r2_hidden @ C @ B ) => ( A @ C ) ) ) ) => ( ( = @ B @ k1_xboole_0 ) | ( A @ B ) ) ) ) ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( A @ B ) ) ) ),file(ordinal2,s1_ordinal2)).
thf(s3_ordinal2,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v5_ordinal1 @ C ) & ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( v1_ordinal2 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( v3_ordinal1 @ D ) => ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ) ),file(ordinal2,s3_ordinal2)).
thf(s1_ordinal4,conjecture,( ( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ A @ B ) => ( r2_hidden @ ( f1_s1_ordinal4 @ A ) @ ( f1_s1_ordinal4 @ B ) ) ) ) ) & ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v4_ordinal1 @ A ) => ( ( = @ A @ k1_xboole_0 ) | ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_ordinal2 @ B ) ) => ( ( ( = @ ( k9_xtuple_0 @ B ) @ A ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( r2_hidden @ C @ A ) => ( = @ ( k1_funct_1 @ B @ C ) @ ( f1_s1_ordinal4 @ C ) ) ) ) ) => ( r1_ordinal2 @ ( f1_s1_ordinal4 @ A ) @ B ) ) ) ) ) ) ) => ? [A: $i] : ( ( v3_ordinal1 @ A ) & ( = @ ( f1_s1_ordinal4 @ A ) @ A ) ) ),file(ordinal4,s1_ordinal4)).
