% Mizar problem: s1_arytm_3,arytm_3,2014,8 
include('Axioms/SET010^2.ax').
thf(n1_type,type,( np__1: $i )).
thf(f1_s1_arytm_3_type,type,( f1_s1_arytm_3: $i )).
thf(f2_s1_arytm_3_type,type,( f2_s1_arytm_3: $i )).
thf(f3_s1_arytm_3_type,type,( f3_s1_arytm_3: $i )).
thf(k10_ordinal2_type,type,( k10_ordinal2: $i > $i > $i )).
thf(k11_arytm_3_type,type,( k11_arytm_3: $i )).
thf(k11_ordinal2_type,type,( k11_ordinal2: $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_tarski_type,type,( k2_tarski: $i > $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k4_xboole_0_type,type,( k4_xboole_0: $i > $i > $i )).
thf(k5_arytm_3_type,type,( k5_arytm_3: $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_arytm_3_type,type,( k6_arytm_3: $i > $i )).
thf(k6_subset_1_type,type,( k6_subset_1: $i > $i > $i )).
thf(k7_arytm_3_type,type,( k7_arytm_3: $i > $i )).
thf(k8_arytm_3_type,type,( k8_arytm_3: $i > $i > $i )).
thf(k8_ordinal3_type,type,( k8_ordinal3: $i > $i > $i )).
thf(k9_arytm_3_type,type,( k9_arytm_3: $i > $i > $i )).
thf(k9_ordinal3_type,type,( k9_ordinal3: $i > $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(p1_s1_arytm_3_type,type,( p1_s1_arytm_3: $i > $o )).
thf(r1_arytm_3_type,type,( r1_arytm_3: $i > $i > $o )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $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(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $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(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_arytm_3,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) => ( ( v3_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ) ),file(arytm_3,cc1_arytm_3)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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(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(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(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
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(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(commutativity_k2_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ B @ A ) ) ),file(tarski,k2_tarski)).
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(commutativity_k8_ordinal3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k8_ordinal3 @ A @ B ) @ ( k8_ordinal3 @ B @ A ) ) ) ),file(ordinal3,k8_ordinal3)).
thf(commutativity_k9_arytm_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( m1_subset_1 @ B @ k5_arytm_3 ) ) => ( = @ ( k9_arytm_3 @ A @ B ) @ ( k9_arytm_3 @ B @ A ) ) ) ),file(arytm_3,k9_arytm_3)).
thf(commutativity_k9_ordinal3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k9_ordinal3 @ A @ B ) @ ( k9_ordinal3 @ B @ A ) ) ) ),file(ordinal3,k9_ordinal3)).
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(d11_arytm_3,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) => ! [B: $i] : ( ( m1_subset_1 @ B @ k5_arytm_3 ) => ( = @ ( k9_arytm_3 @ A @ B ) @ ( k8_arytm_3 @ ( k8_ordinal3 @ ( k9_ordinal3 @ ( k6_arytm_3 @ A ) @ ( k7_arytm_3 @ B ) ) @ ( k9_ordinal3 @ ( k6_arytm_3 @ B ) @ ( k7_arytm_3 @ A ) ) ) @ ( k9_ordinal3 @ ( k7_arytm_3 @ A ) @ ( k7_arytm_3 @ B ) ) ) ) ) ) ),file(arytm_3,d11_arytm_3)).
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(d1_ordinal1,axiom,( ! [A: $i] : ( = @ ( k1_ordinal1 @ A ) @ ( k2_xboole_0 @ A @ ( k1_tarski @ A ) ) ) ),file(ordinal1,d1_ordinal1)).
thf(d5_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k4_tarski @ A @ B ) @ ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ) ),file(tarski,d5_tarski)).
thf(d7_arytm_3,axiom,( = @ k5_arytm_3 @ ( k2_xboole_0 @ ( k6_subset_1 @ ( replSep2 @ ^ [A: $i] : ( m1_subset_1 @ A @ k4_ordinal1 ) @ ^ [A: $i] : ^ [B: $i] : ( m1_subset_1 @ B @ k4_ordinal1 ) @ ^ [A: $i] : ^ [B: $i] : ( k4_tarski @ A @ B ) @ ^ [A: $i] : ^ [B: $i] : ( ( r1_arytm_3 @ A @ B ) & ~ ( = @ B @ k1_xboole_0 ) ) ) @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ k4_ordinal1 ) @ ^ [A: $i] : ( k4_tarski @ A @ np__1 ) @ ^ [A: $i] : $true ) ) @ k4_ordinal1 ) ),file(arytm_3,d7_arytm_3)).
thf(dt_f1_s1_arytm_3,axiom,( m1_subset_1 @ f1_s1_arytm_3 @ k5_arytm_3 ),file(arytm_3,f1_s1_arytm_3)).
thf(dt_f2_s1_arytm_3,axiom,( m1_subset_1 @ f2_s1_arytm_3 @ k5_arytm_3 ),file(arytm_3,f2_s1_arytm_3)).
thf(dt_f3_s1_arytm_3,axiom,( m1_subset_1 @ f3_s1_arytm_3 @ k5_arytm_3 ),file(arytm_3,f3_s1_arytm_3)).
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_k11_arytm_3,axiom,( m1_subset_1 @ k11_arytm_3 @ k5_arytm_3 ),file(arytm_3,k11_arytm_3)).
thf(dt_k11_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k11_ordinal2 @ A @ B ) ) ) ),file(ordinal2,k11_ordinal2)).
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_tarski,axiom,( $true ),file(tarski,k2_tarski)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_k4_xboole_0,axiom,( $true ),file(xboole_0,k4_xboole_0)).
thf(dt_k5_arytm_3,axiom,( $true ),file(arytm_3,k5_arytm_3)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k6_arytm_3,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) => ( m1_subset_1 @ ( k6_arytm_3 @ A ) @ k4_ordinal1 ) ) ),file(arytm_3,k6_arytm_3)).
thf(dt_k6_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( m1_subset_1 @ ( k6_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,k6_subset_1)).
thf(dt_k7_arytm_3,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) => ( m1_subset_1 @ ( k7_arytm_3 @ A ) @ k4_ordinal1 ) ) ),file(arytm_3,k7_arytm_3)).
thf(dt_k8_arytm_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) ) => ( m1_subset_1 @ ( k8_arytm_3 @ A @ B ) @ k5_arytm_3 ) ) ),file(arytm_3,k8_arytm_3)).
thf(dt_k8_ordinal3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k8_ordinal3 @ A @ B ) ) ) ),file(ordinal3,k8_ordinal3)).
thf(dt_k9_arytm_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( m1_subset_1 @ B @ k5_arytm_3 ) ) => ( m1_subset_1 @ ( k9_arytm_3 @ A @ B ) @ k5_arytm_3 ) ) ),file(arytm_3,k9_arytm_3)).
thf(dt_k9_ordinal3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k9_ordinal3 @ A @ B ) ) ) ),file(ordinal3,k9_ordinal3)).
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(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_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
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_xboole_0,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ) ),file(xboole_0,fc2_xboole_0)).
thf(fc3_arytm_3,axiom,( ~ ( v1_xboole_0 @ k5_arytm_3 ) ),file(arytm_3,fc3_arytm_3)).
thf(fc3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ) ),file(xboole_0,fc3_xboole_0)).
thf(fc4_ordinal3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) ) => ( ( v3_ordinal1 @ ( k11_ordinal2 @ A @ B ) ) & ( v7_ordinal1 @ ( k11_ordinal2 @ A @ B ) ) ) ) ),file(ordinal3,fc4_ordinal3)).
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_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_ordinal1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) => ( v7_ordinal1 @ ( k1_ordinal1 @ A ) ) ) ),file(ordinal1,fc7_ordinal1)).
thf(idempotence_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k2_xboole_0)).
thf(l43_arytm_3,axiom,( r1_tarski @ k4_ordinal1 @ k5_arytm_3 ),file(arytm_3,l43_arytm_3)).
thf(rc1_arytm_3,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ~ ( v1_xboole_0 @ A ) & ( v3_ordinal1 @ A ) ) ),file(arytm_3,rc1_arytm_3)).
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_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_arytm_3,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( v1_xboole_0 @ A ) ) ),file(arytm_3,rc2_arytm_3)).
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_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(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_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
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(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(redefinition_k11_arytm_3,axiom,( = @ k11_arytm_3 @ k1_xboole_0 ),file(arytm_3,k11_arytm_3)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_k6_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k6_subset_1 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ) ),file(subset_1,k6_subset_1)).
thf(redefinition_k8_ordinal3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k8_ordinal3 @ A @ B ) @ ( k10_ordinal2 @ A @ B ) ) ) ),file(ordinal3,k8_ordinal3)).
thf(redefinition_k9_ordinal3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k9_ordinal3 @ A @ B ) @ ( k11_ordinal2 @ A @ B ) ) ) ),file(ordinal3,k9_ordinal3)).
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(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(symmetry_r1_arytm_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_arytm_3 @ A @ B ) => ( r1_arytm_3 @ B @ A ) ) ) ),file(arytm_3,r1_arytm_3)).
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(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(t29_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ~ ( ~ ( v4_ordinal1 @ A ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ~ ( = @ A @ ( k1_ordinal1 @ B ) ) ) ) & ~ ( ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( = @ A @ ( k1_ordinal1 @ B ) ) ) & ( v4_ordinal1 @ A ) ) ) ) ),file(ordinal1,t29_ordinal1)).
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(t31_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( = @ ( k10_ordinal2 @ A @ np__1 ) @ ( k1_ordinal1 @ A ) ) ) ),file(ordinal2,t31_ordinal2)).
thf(t3_boole,axiom,( ! [A: $i] : ( = @ ( k4_xboole_0 @ A @ k1_xboole_0 ) @ A ) ),file(boole,t3_boole)).
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_boole,axiom,( ! [A: $i] : ( = @ ( k4_xboole_0 @ k1_xboole_0 @ A ) @ k1_xboole_0 ) ),file(boole,t4_boole)).
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(t58_arytm_3,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( m1_subset_1 @ A @ k5_arytm_3 ) ) => ! [B: $i] : ( ( ( v3_ordinal1 @ B ) & ( m1_subset_1 @ B @ k5_arytm_3 ) ) => ( = @ ( k9_arytm_3 @ A @ B ) @ ( k8_ordinal3 @ A @ B ) ) ) ) ),file(arytm_3,t58_arytm_3)).
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(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_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ ( k1_ordinal1 @ B ) ) <=> ( ( r2_hidden @ A @ B ) | ( = @ A @ B ) ) ) ),file(ordinal1,t8_ordinal1)).
thf(t8_ordinal3,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ~ ( = @ A @ k1_xboole_0 ) => ( r2_hidden @ k1_xboole_0 @ A ) ) ) ),file(ordinal3,t8_ordinal3)).
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_arytm_3,conjecture,( ( ( = @ f2_s1_arytm_3 @ np__1 ) & ( = @ f1_s1_arytm_3 @ k11_arytm_3 ) & ( r2_hidden @ f3_s1_arytm_3 @ k4_ordinal1 ) & ( p1_s1_arytm_3 @ f1_s1_arytm_3 ) & ~ ( p1_s1_arytm_3 @ f3_s1_arytm_3 ) ) => ? [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( r2_hidden @ A @ k4_ordinal1 ) & ( p1_s1_arytm_3 @ A ) & ~ ( p1_s1_arytm_3 @ ( k9_arytm_3 @ A @ f2_s1_arytm_3 ) ) ) ),file(arytm_3,s1_arytm_3)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
