% Mizar problem: e16_60_1_2_4_2_2,arytm_2,2348,28 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_60_type,type,( c1_60__arytm_2: $i )).
thf(c3_60_1_2_4_2_2_type,type,( c3_60_1_2_4_2_2__arytm_2: $i )).
thf(c4_60_1_2_type,type,( c4_60_1_2__arytm_2: $i )).
thf(c6_60_1_2_4_2_2_type,type,( c6_60_1_2_4_2_2__arytm_2: $i )).
thf(k10_arytm_3_type,type,( k10_arytm_3: $i > $i > $i )).
thf(k11_arytm_3_type,type,( k11_arytm_3: $i )).
thf(k12_arytm_3_type,type,( k12_arytm_3: $i )).
thf(k1_arytm_2_type,type,( k1_arytm_2: $i )).
thf(k1_arytm_3_type,type,( k1_arytm_3: $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_arytm_3_type,type,( k5_arytm_3: $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k9_arytm_3_type,type,( k9_arytm_3: $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(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(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(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(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
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(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
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(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(dt_k1_arytm_3,axiom,( $true ),file(arytm_3,k1_arytm_3)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
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_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal2,cc2_ordinal2)).
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(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
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_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_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(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(commutativity_k10_arytm_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( m1_subset_1 @ B @ k5_arytm_3 ) ) => ( = @ ( k10_arytm_3 @ A @ B ) @ ( k10_arytm_3 @ B @ A ) ) ) ),file(arytm_3,k10_arytm_3)).
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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k11_arytm_3,axiom,( = @ k11_arytm_3 @ k1_xboole_0 ),file(arytm_3,k11_arytm_3)).
thf(redefinition_k12_arytm_3,axiom,( = @ k12_arytm_3 @ k1_arytm_3 ),file(arytm_3,k12_arytm_3)).
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(dt_k10_arytm_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( m1_subset_1 @ B @ k5_arytm_3 ) ) => ( m1_subset_1 @ ( k10_arytm_3 @ A @ B ) @ k5_arytm_3 ) ) ),file(arytm_3,k10_arytm_3)).
thf(dt_k11_arytm_3,axiom,( m1_subset_1 @ k11_arytm_3 @ k5_arytm_3 ),file(arytm_3,k11_arytm_3)).
thf(dt_k12_arytm_3,axiom,( ~ ( v1_xboole_0 @ k12_arytm_3 ) & ( v3_ordinal1 @ k12_arytm_3 ) & ( m1_subset_1 @ k12_arytm_3 @ k5_arytm_3 ) ),file(arytm_3,k12_arytm_3)).
thf(dt_k1_arytm_2,axiom,( m1_subset_1 @ k1_arytm_2 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ k5_arytm_3 ) ) ),file(arytm_2,k1_arytm_2)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k5_arytm_3,axiom,( $true ),file(arytm_3,k5_arytm_3)).
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_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(dt_c1_60__arytm_2,axiom,( m2_subset_1 @ c1_60__arytm_2 @ ( k1_zfmisc_1 @ k5_arytm_3 ) @ k1_arytm_2 ),file(arytm_2,c1_60__arytm_2)).
thf(dt_c3_60_1_2_4_2_2__arytm_2,axiom,( m1_subset_1 @ c3_60_1_2_4_2_2__arytm_2 @ k5_arytm_3 ),file(arytm_2,c3_60_1_2_4_2_2__arytm_2)).
thf(dt_c4_60_1_2__arytm_2,axiom,( m1_subset_1 @ c4_60_1_2__arytm_2 @ k5_arytm_3 ),file(arytm_2,c4_60_1_2__arytm_2)).
thf(dt_c6_60_1_2_4_2_2__arytm_2,axiom,( m1_subset_1 @ c6_60_1_2_4_2_2__arytm_2 @ k5_arytm_3 ),file(arytm_2,c6_60_1_2_4_2_2__arytm_2)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(fc1_arytm_2,axiom,( ~ ( v1_xboole_0 @ k1_arytm_2 ) ),file(arytm_2,fc1_arytm_2)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc3_arytm_3,axiom,( ~ ( v1_xboole_0 @ k5_arytm_3 ) ),file(arytm_3,fc3_arytm_3)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
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(l51_arytm_2,axiom,( = @ k12_arytm_3 @ np__1 ),file(arytm_2,l51_arytm_2)).
thf(l52_arytm_2,axiom,( = @ k11_arytm_3 @ k11_arytm_3 ),file(arytm_2,l52_arytm_2)).
thf(e12_60_1_2_4_2_2__arytm_2,axiom,( r2_hidden @ c6_60_1_2_4_2_2__arytm_2 @ k4_ordinal1 ),file(arytm_2,e12_60_1_2_4_2_2__arytm_2)).
thf(e14_60_1_2_4_2_2__arytm_2,axiom,( r2_hidden @ ( k10_arytm_3 @ k11_arytm_3 @ ( k10_arytm_3 @ c4_60_1_2__arytm_2 @ c3_60_1_2_4_2_2__arytm_2 ) ) @ c1_60__arytm_2 ),file(arytm_2,e14_60_1_2_4_2_2__arytm_2)).
thf(e15_60_1_2_4_2_2__arytm_2,axiom,( ~ ( r2_hidden @ ( k10_arytm_3 @ c6_60_1_2_4_2_2__arytm_2 @ ( k10_arytm_3 @ c4_60_1_2__arytm_2 @ c3_60_1_2_4_2_2__arytm_2 ) ) @ c1_60__arytm_2 ) ),file(arytm_2,e15_60_1_2_4_2_2__arytm_2)).
thf(s1_arytm_3,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( = @ D @ np__1 ) & ( = @ C @ k11_arytm_3 ) & ( r2_hidden @ B @ k4_ordinal1 ) & ( A @ C ) & ~ ( A @ B ) ) => ? [E: $i] : ( ( m1_subset_1 @ E @ k5_arytm_3 ) & ( r2_hidden @ E @ k4_ordinal1 ) & ( A @ E ) & ~ ( A @ ( k9_arytm_3 @ E @ D ) ) ) ) ),file(arytm_3,s1_arytm_3)).
thf(e16_60_1_2_4_2_2__arytm_2,conjecture,( ? [A: $i] : ( ( m1_subset_1 @ A @ k5_arytm_3 ) & ( r2_hidden @ A @ k4_ordinal1 ) & ( r2_hidden @ ( k10_arytm_3 @ A @ ( k10_arytm_3 @ c4_60_1_2__arytm_2 @ c3_60_1_2_4_2_2__arytm_2 ) ) @ c1_60__arytm_2 ) & ~ ( r2_hidden @ ( k10_arytm_3 @ ( k9_arytm_3 @ A @ k12_arytm_3 ) @ ( k10_arytm_3 @ c4_60_1_2__arytm_2 @ c3_60_1_2_4_2_2__arytm_2 ) ) @ c1_60__arytm_2 ) ) ),file(arytm_2,e16_60_1_2_4_2_2__arytm_2)).
