% Mizar problem: e4_30,domain_1,495,17 
include('Axioms/SET010^4.ax').
thf(c1_30_type,type,( c1_30__domain_1: $i )).
thf(c2_30_type,type,( c2_30__domain_1: $i )).
thf(c3_30_type,type,( c3_30__domain_1: $i )).
thf(c4_30_type,type,( c4_30__domain_1: $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(k3_xtuple_0_type,type,( k3_xtuple_0: $i > $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k4_zfmisc_1_type,type,( k4_zfmisc_1: $i > $i > $i > $i > $i )).
thf(k5_domain_1_type,type,( k5_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i )).
thf(k6_xtuple_0_type,type,( k6_xtuple_0: $i > $i > $i > $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $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_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_xtuple_0_type,type,( v2_xtuple_0: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v3_xtuple_0_type,type,( v3_xtuple_0: $i > $o )).
thf(commutativity_k2_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ B @ A ) ) ),file(tarski,k2_tarski)).
thf(dt_k1_tarski,axiom,( $true ),file(tarski,k1_tarski)).
thf(dt_k2_tarski,axiom,( $true ),file(tarski,k2_tarski)).
thf(cc1_xtuple_0,axiom,( ! [A: $i] : ( ( v2_xtuple_0 @ A ) => ( v1_xtuple_0 @ A ) ) ),file(xtuple_0,cc1_xtuple_0)).
thf(fc2_xboole_0,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ) ),file(xboole_0,fc2_xboole_0)).
thf(fc3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ) ),file(xboole_0,fc3_xboole_0)).
thf(fc5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ) ),file(relat_1,fc5_relat_1)).
thf(fc7_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ) ),file(relat_1,fc7_relat_1)).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc2_xtuple_0,axiom,( ? [A: $i] : ( v2_xtuple_0 @ A ) ),file(xtuple_0,rc2_xtuple_0)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k3_xtuple_0,axiom,( $true ),file(xtuple_0,k3_xtuple_0)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(cc2_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_relat_1 @ B ) ) ) ),file(relat_1,cc2_relat_1)).
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(cc2_xtuple_0,axiom,( ! [A: $i] : ( ( v3_xtuple_0 @ A ) => ( v2_xtuple_0 @ A ) ) ),file(xtuple_0,cc2_xtuple_0)).
thf(cc3_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) ) ),file(relat_1,cc3_relat_1)).
thf(cc4_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ) ),file(relat_1,cc4_relat_1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc2_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( v2_xtuple_0 @ ( k3_xtuple_0 @ A @ B @ C ) ) ),file(xtuple_0,fc2_xtuple_0)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_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(rc3_xtuple_0,axiom,( ? [A: $i] : ( v3_xtuple_0 @ A ) ),file(xtuple_0,rc3_xtuple_0)).
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(d2_xboole_0,axiom,( = @ k1_xboole_0 @ ( eps @ ^ [A: $i] : ( v1_xboole_0 @ A ) ) ),file(xboole_0,d2_xboole_0)).
thf(d4_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( = @ ( k3_xtuple_0 @ A @ B @ C ) @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) ) ),file(xtuple_0,d4_xtuple_0)).
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(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(dt_k6_xtuple_0,axiom,( $true ),file(xtuple_0,k6_xtuple_0)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_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(cc2_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) => ( v3_xtuple_0 @ E ) ) ) ),file(mcart_1,cc2_mcart_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_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(fc12_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) ) => ~ ( v1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),file(subset_1,fc12_subset_1)).
thf(fc3_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( v3_xtuple_0 @ ( k6_xtuple_0 @ A @ B @ C @ D ) ) ),file(xtuple_0,fc3_xtuple_0)).
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(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(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(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
thf(d8_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( = @ ( k6_xtuple_0 @ A @ B @ C @ D ) @ ( k4_tarski @ ( k3_xtuple_0 @ A @ B @ C ) @ D ) ) ),file(xtuple_0,d8_xtuple_0)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(redefinition_k5_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ! [G: $i] : ! [H: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) & ( m1_subset_1 @ G @ C ) & ( m1_subset_1 @ H @ D ) ) => ( = @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k6_xtuple_0 @ E @ F @ G @ H ) ) ) ),file(domain_1,k5_domain_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k4_zfmisc_1,axiom,( $true ),file(zfmisc_1,k4_zfmisc_1)).
thf(dt_k5_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ! [G: $i] : ! [H: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) & ( m1_subset_1 @ G @ C ) & ( m1_subset_1 @ H @ D ) ) => ( m1_subset_1 @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),file(domain_1,k5_domain_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_30__domain_1,axiom,( ~ ( v1_xboole_0 @ c1_30__domain_1 ) ),file(domain_1,c1_30__domain_1)).
thf(dt_c2_30__domain_1,axiom,( ~ ( v1_xboole_0 @ c2_30__domain_1 ) ),file(domain_1,c2_30__domain_1)).
thf(dt_c3_30__domain_1,axiom,( ~ ( v1_xboole_0 @ c3_30__domain_1 ) ),file(domain_1,c3_30__domain_1)).
thf(dt_c4_30__domain_1,axiom,( ~ ( v1_xboole_0 @ c4_30__domain_1 ) ),file(domain_1,c4_30__domain_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_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(t7_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t7_boole)).
thf(e3_30__domain_1,axiom,( m1_subset_1 @ ( replSep4 @ ^ [A: $i] : ( m1_subset_1 @ A @ c1_30__domain_1 ) @ ^ [A: $i] : ^ [B: $i] : ( m1_subset_1 @ B @ c2_30__domain_1 ) @ ^ [A: $i] : ^ [B: $i] : ^ [C: $i] : ( m1_subset_1 @ C @ c3_30__domain_1 ) @ ^ [A: $i] : ^ [B: $i] : ^ [C: $i] : ^ [D: $i] : ( m1_subset_1 @ D @ c4_30__domain_1 ) @ ^ [A: $i] : ^ [B: $i] : ^ [C: $i] : ^ [D: $i] : ( k5_domain_1 @ c1_30__domain_1 @ c2_30__domain_1 @ c3_30__domain_1 @ c4_30__domain_1 @ A @ B @ C @ D ) @ ^ [A: $i] : ^ [B: $i] : ^ [C: $i] : ^ [D: $i] : $true ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ c1_30__domain_1 @ c2_30__domain_1 @ c3_30__domain_1 @ c4_30__domain_1 ) ) ),file(domain_1,e3_30__domain_1)).
thf(e1_30__domain_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k4_zfmisc_1 @ c1_30__domain_1 @ c2_30__domain_1 @ c3_30__domain_1 @ c4_30__domain_1 ) ) => ( r2_hidden @ A @ ( replSep4 @ ^ [B: $i] : ( m1_subset_1 @ B @ c1_30__domain_1 ) @ ^ [B: $i] : ^ [C: $i] : ( m1_subset_1 @ C @ c2_30__domain_1 ) @ ^ [B: $i] : ^ [C: $i] : ^ [D: $i] : ( m1_subset_1 @ D @ c3_30__domain_1 ) @ ^ [B: $i] : ^ [C: $i] : ^ [D: $i] : ^ [E: $i] : ( m1_subset_1 @ E @ c4_30__domain_1 ) @ ^ [B: $i] : ^ [C: $i] : ^ [D: $i] : ^ [E: $i] : ( k5_domain_1 @ c1_30__domain_1 @ c2_30__domain_1 @ c3_30__domain_1 @ c4_30__domain_1 @ B @ C @ D @ E ) @ ^ [B: $i] : ^ [C: $i] : ^ [D: $i] : ^ [E: $i] : $true ) ) ) ),file(domain_1,e1_30__domain_1)).
thf(t28_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ! [C: $i] : ( ( m1_subset_1 @ C @ A ) => ( r2_hidden @ C @ B ) ) => ( = @ A @ B ) ) ) ),file(subset_1,t28_subset_1)).
thf(e4_30__domain_1,conjecture,( = @ ( k4_zfmisc_1 @ c1_30__domain_1 @ c2_30__domain_1 @ c3_30__domain_1 @ c4_30__domain_1 ) @ ( replSep4 @ ^ [A: $i] : ( m1_subset_1 @ A @ c1_30__domain_1 ) @ ^ [A: $i] : ^ [B: $i] : ( m1_subset_1 @ B @ c2_30__domain_1 ) @ ^ [A: $i] : ^ [B: $i] : ^ [C: $i] : ( m1_subset_1 @ C @ c3_30__domain_1 ) @ ^ [A: $i] : ^ [B: $i] : ^ [C: $i] : ^ [D: $i] : ( m1_subset_1 @ D @ c4_30__domain_1 ) @ ^ [A: $i] : ^ [B: $i] : ^ [C: $i] : ^ [D: $i] : ( k5_domain_1 @ c1_30__domain_1 @ c2_30__domain_1 @ c3_30__domain_1 @ c4_30__domain_1 @ A @ B @ C @ D ) @ ^ [A: $i] : ^ [B: $i] : ^ [C: $i] : ^ [D: $i] : $true ) ),file(domain_1,e4_30__domain_1)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
