% Mizar problem: e4_30_1_1_1,heyting1,711,34 
include('Axioms/SET010^0.ax').
thf(c1_30_type,type,( c1_30__heyting1: $i )).
thf(c2_30_type,type,( c2_30__heyting1: $i )).
thf(c3_30_type,type,( c3_30__heyting1: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_funct_2_type,type,( k1_funct_2: $i > $i > $i )).
thf(k1_heyting1_type,type,( k1_heyting1: $i > $i )).
thf(k1_xtuple_0_type,type,( k1_xtuple_0: $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_domain_1_type,type,( k2_domain_1: $i > $i > $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k2_xtuple_0_type,type,( k2_xtuple_0: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_domain_1_type,type,( k3_domain_1: $i > $i > $i > $i )).
thf(k3_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k3_xboole_0_type,type,( k3_xboole_0: $i > $i > $i )).
thf(k5_finsub_1_type,type,( k5_finsub_1: $i > $i )).
thf(k7_normform_type,type,( k7_normform: $i > $i )).
thf(k8_normform_type,type,( k8_normform: $i > $i )).
thf(k9_funct_2_type,type,( k9_funct_2: $i > $i > $i )).
thf(m1_funct_2_type,type,( m1_funct_2: $i > $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_funct_2_type,type,( m2_funct_2: $i > $i > $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_finsub_1_type,type,( v1_finsub_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_funct_2_type,type,( v1_funct_2: $i > $i > $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $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_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v3_finsub_1_type,type,( v3_finsub_1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v4_finsub_1_type,type,( v4_finsub_1: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(cc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_partfun1 @ C @ A ) => ( v1_funct_2 @ C @ A @ B ) ) ) ),file(funct_2,cc1_funct_2)).
thf(cc2_finsub_1,axiom,( ! [A: $i] : ( ( ( v1_finsub_1 @ A ) & ( v3_finsub_1 @ A ) ) => ( v4_finsub_1 @ A ) ) ),file(finsub_1,cc2_finsub_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(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v4_relat_1 @ C @ A ) ) ) ),file(relat_1,cc5_relat_1)).
thf(cc5_subset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,cc5_subset_1)).
thf(cc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v5_relat_1 @ C @ A ) ) ) ),file(relat_1,cc6_relat_1)).
thf(cc7_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc7_finset_1)).
thf(cc7_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc7_relat_1)).
thf(cc8_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_finset_1 @ B ) ) ) ),file(finset_1,cc8_finset_1)).
thf(cc8_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc8_relat_1)).
thf(fc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) ) => ( v4_relat_1 @ ( k2_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc1_relset_1)).
thf(fc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) ) => ( v4_relat_1 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc2_relset_1)).
thf(fc33_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_finset_1 @ A ) & ( v5_finset_1 @ B ) ) => ( v5_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(finset_1,fc33_finset_1)).
thf(fc35_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) => ( v1_finset_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(finset_1,fc35_finset_1)).
thf(fc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) ) => ( v5_relat_1 @ ( k2_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc4_relset_1)).
thf(fc5_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) ) => ( v5_relat_1 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc5_relset_1)).
thf(rc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ),file(funct_2,rc1_funct_2)).
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(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relat_1,rc3_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(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_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ),file(finset_1,rc5_finset_1)).
thf(rc5_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc5_subset_1)).
thf(rc6_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ) ),file(finset_1,rc6_finset_1)).
thf(rc6_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc6_subset_1)).
thf(rc7_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc7_finset_1)).
thf(rc8_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(rc9_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) ),file(finset_1,rc9_finset_1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_funct_2,axiom,( $true ),file(funct_2,k1_funct_2)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_m1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_funct_2 @ C @ A @ B ) => ~ ( v1_xboole_0 @ C ) ) ),file(funct_2,m1_funct_2)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_finsub_1,axiom,( ! [A: $i] : ( ( v4_finsub_1 @ A ) => ( ( v1_finsub_1 @ A ) & ( v3_finsub_1 @ A ) ) ) ),file(finsub_1,cc1_finsub_1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_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(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_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc2_finset_1)).
thf(cc2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc2_funct_2)).
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_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(cc3_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( v1_finset_1 @ C ) ) ) ) ) ),file(finset_1,cc3_finset_1)).
thf(cc3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc3_funct_2)).
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(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_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_funct_2 @ B @ A @ A ) => ( v1_partfun1 @ B @ A ) ) ) ),file(funct_2,cc4_funct_2)).
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(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(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
thf(cc8_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ~ ( v1_xboole_0 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ),file(funct_2,cc8_funct_2)).
thf(cc9_finset_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_finset_1 @ A ) ) ) ),file(finset_1,cc9_finset_1)).
thf(cc9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_funct_2 @ C @ A @ B ) => ( v4_funct_1 @ C ) ) ),file(funct_2,cc9_funct_2)).
thf(fc10_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ B ) => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(finset_1,fc10_finset_1)).
thf(fc10_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( v4_funct_1 @ ( k1_funct_2 @ A @ B ) ) ),file(funct_2,fc10_funct_2)).
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(fc11_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(finset_1,fc11_finset_1)).
thf(fc14_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(finset_1,fc14_finset_1)).
thf(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_1)).
thf(fc1_finsub_1,axiom,( ! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),file(finsub_1,fc1_finsub_1)).
thf(fc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ) ),file(funct_2,fc1_funct_2)).
thf(fc1_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(relat_1,fc1_relat_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc2_funct_2,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ) ),file(funct_2,fc2_funct_2)).
thf(fc31_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc31_finset_1)).
thf(fc3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xboole_0 @ B ) ) => ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ) ),file(funct_2,fc3_funct_2)).
thf(fc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) ) => ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(relat_1,fc3_relat_1)).
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_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(fc9_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(finset_1,fc9_finset_1)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_heyting1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k8_normform @ A ) ) & ~ ( v1_xboole_0 @ B ) ) ),file(heyting1,rc1_heyting1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_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_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc2_finset_1)).
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_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc3_finset_1)).
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(idempotence_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k2_xboole_0)).
thf(commutativity_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ A ) ) ),file(xboole_0,k3_xboole_0)).
thf(idempotence_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k3_xboole_0)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k2_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( = @ ( k2_domain_1 @ A @ B @ C ) @ ( k1_xtuple_0 @ C ) ) ) ),file(domain_1,k2_domain_1)).
thf(redefinition_k3_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( = @ ( k3_domain_1 @ A @ B @ C ) @ ( k2_xtuple_0 @ C ) ) ) ),file(domain_1,k3_domain_1)).
thf(redefinition_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(funct_2,k3_funct_2)).
thf(redefinition_k9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( = @ ( k9_funct_2 @ A @ B ) @ ( k1_funct_2 @ A @ B ) ) ) ),file(funct_2,k9_funct_2)).
thf(redefinition_m2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( m1_funct_2 @ C @ A @ B ) ) => ! [D: $i] : ( ( m2_funct_2 @ D @ A @ B @ C ) <=> ( m1_subset_1 @ D @ C ) ) ) ),file(funct_2,m2_funct_2)).
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_k1_heyting1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_heyting1 @ A ) ) ),file(heyting1,k1_heyting1)).
thf(dt_k1_xtuple_0,axiom,( $true ),file(xtuple_0,k1_xtuple_0)).
thf(dt_k2_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( m1_subset_1 @ ( k2_domain_1 @ A @ B @ C ) @ A ) ) ),file(domain_1,k2_domain_1)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
thf(dt_k2_xtuple_0,axiom,( $true ),file(xtuple_0,k2_xtuple_0)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( m1_subset_1 @ ( k3_domain_1 @ A @ B @ C ) @ B ) ) ),file(domain_1,k3_domain_1)).
thf(dt_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ B ) ) ),file(funct_2,k3_funct_2)).
thf(dt_k3_xboole_0,axiom,( $true ),file(xboole_0,k3_xboole_0)).
thf(dt_k5_finsub_1,axiom,( ! [A: $i] : ( v4_finsub_1 @ ( k5_finsub_1 @ A ) ) ),file(finsub_1,k5_finsub_1)).
thf(dt_k7_normform,axiom,( ! [A: $i] : ( m1_subset_1 @ ( k7_normform @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) ) ) ),file(normform,k7_normform)).
thf(dt_k8_normform,axiom,( ! [A: $i] : ( m1_subset_1 @ ( k8_normform @ A ) @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ ( k7_normform @ A ) ) ) ) ),file(normform,k8_normform)).
thf(dt_k9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( m1_funct_2 @ ( k9_funct_2 @ A @ B ) @ A @ B ) ) ),file(funct_2,k9_funct_2)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( m1_funct_2 @ C @ A @ B ) ) => ! [D: $i] : ( ( m2_funct_2 @ D @ A @ B @ C ) => ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),file(funct_2,m2_funct_2)).
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_30__heyting1,axiom,( $true ),file(heyting1,c1_30__heyting1)).
thf(dt_c2_30__heyting1,axiom,( m2_subset_1 @ c2_30__heyting1 @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_30__heyting1 ) @ ( k5_finsub_1 @ c1_30__heyting1 ) ) @ ( k7_normform @ c1_30__heyting1 ) ),file(heyting1,c2_30__heyting1)).
thf(dt_c3_30__heyting1,axiom,( m2_subset_1 @ c3_30__heyting1 @ ( k5_finsub_1 @ ( k7_normform @ c1_30__heyting1 ) ) @ ( k8_normform @ c1_30__heyting1 ) ),file(heyting1,c3_30__heyting1)).
thf(cc3_finsub_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) => ( v1_finset_1 @ B ) ) ),file(finsub_1,cc3_finsub_1)).
thf(fc2_finsub_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ ( k5_finsub_1 @ A ) ) & ( v4_finsub_1 @ ( k5_finsub_1 @ A ) ) ) ),file(finsub_1,fc2_finsub_1)).
thf(fc2_normform,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k7_normform @ A ) ) ),file(normform,fc2_normform)).
thf(fc3_normform,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k8_normform @ A ) ) ),file(normform,fc3_normform)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(e3_30_1_1_1__heyting1,axiom,( ! [A: $i] : ( ( m2_subset_1 @ A @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_30__heyting1 ) @ ( k5_finsub_1 @ c1_30__heyting1 ) ) @ ( k7_normform @ c1_30__heyting1 ) ) => ~ ( ( r2_hidden @ A @ c3_30__heyting1 ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_heyting1 @ c1_30__heyting1 ) ) => ~ ( r2_hidden @ B @ ( k2_xboole_0 @ ( k3_xboole_0 @ ( k1_xtuple_0 @ A ) @ ( k3_domain_1 @ ( k5_finsub_1 @ c1_30__heyting1 ) @ ( k5_finsub_1 @ c1_30__heyting1 ) @ c2_30__heyting1 ) ) @ ( k3_xboole_0 @ ( k2_xtuple_0 @ A ) @ ( k2_domain_1 @ ( k5_finsub_1 @ c1_30__heyting1 ) @ ( k5_finsub_1 @ c1_30__heyting1 ) @ c2_30__heyting1 ) ) ) ) ) ) ) ),file(heyting1,e3_30_1_1_1__heyting1)).
thf(s27_fraenkel,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ! [E: $i] : ( ( m1_subset_1 @ E @ D ) => ~ ( ( r2_hidden @ E @ C ) & ! [F: $i] : ( ( m1_subset_1 @ F @ B ) => ~ ( A @ E @ F ) ) ) ) => ? [E: $i] : ( ( m2_funct_2 @ E @ D @ B @ ( k9_funct_2 @ D @ B ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ( ( r2_hidden @ F @ C ) => ( A @ F @ ( k3_funct_2 @ D @ B @ E @ F ) ) ) ) ) ) ),file(fraenkel,s27_fraenkel)).
thf(e4_30_1_1_1__heyting1,conjecture,( ? [A: $i] : ( ( m2_funct_2 @ A @ ( k7_normform @ c1_30__heyting1 ) @ ( k1_heyting1 @ c1_30__heyting1 ) @ ( k9_funct_2 @ ( k7_normform @ c1_30__heyting1 ) @ ( k1_heyting1 @ c1_30__heyting1 ) ) ) & ! [B: $i] : ( ( m2_subset_1 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ c1_30__heyting1 ) @ ( k5_finsub_1 @ c1_30__heyting1 ) ) @ ( k7_normform @ c1_30__heyting1 ) ) => ( ( r2_hidden @ B @ c3_30__heyting1 ) => ( r2_hidden @ ( k3_funct_2 @ ( k7_normform @ c1_30__heyting1 ) @ ( k1_heyting1 @ c1_30__heyting1 ) @ A @ B ) @ ( k2_xboole_0 @ ( k3_xboole_0 @ ( k1_xtuple_0 @ B ) @ ( k3_domain_1 @ ( k5_finsub_1 @ c1_30__heyting1 ) @ ( k5_finsub_1 @ c1_30__heyting1 ) @ c2_30__heyting1 ) ) @ ( k3_xboole_0 @ ( k2_xtuple_0 @ B ) @ ( k2_domain_1 @ ( k5_finsub_1 @ c1_30__heyting1 ) @ ( k5_finsub_1 @ c1_30__heyting1 ) @ c2_30__heyting1 ) ) ) ) ) ) ) ),file(heyting1,e4_30_1_1_1__heyting1)).
