% Mizar problem: e2_22,heyting2,654,65 
include('Axioms/SET010^1.ax').
thf(c1_22_type,type,( c1_22__heyting2: $i )).
thf(c2_22_type,type,( c2_22__heyting2: $i )).
thf(c3_22_type,type,( c3_22__heyting2: $i )).
thf(k1_tarski_type,type,( k1_tarski: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k4_partfun1_type,type,( k4_partfun1: $i > $i > $i )).
thf(k5_finsub_1_type,type,( k5_finsub_1: $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(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_finsub_1_type,type,( v1_finsub_1: $i > $o )).
thf(v1_funcop_1_type,type,( v1_funcop_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_pre_poly_type,type,( v1_pre_poly: $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_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_pre_poly_type,type,( v2_pre_poly: $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_funct_1_type,type,( v3_funct_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(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(cc4_pre_poly,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_pre_poly @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ) ),file(pre_poly,cc4_pre_poly)).
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(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_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc3_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc3_funct_1)).
thf(rc4_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc4_funct_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(rc7_pre_poly,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_pre_poly @ A ) ) ),file(pre_poly,rc7_pre_poly)).
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(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_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(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_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_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(cc5_pre_poly,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_pre_poly @ A ) ) ) ),file(pre_poly,cc5_pre_poly)).
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(cc7_pre_poly,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_pre_poly @ A ) ) ) ),file(pre_poly,cc7_pre_poly)).
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(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(fc19_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_finset_1 @ A ) ) => ( v1_finset_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(finset_1,fc19_finset_1)).
thf(fc24_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc24_relat_1)).
thf(fc8_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc8_relat_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(rc2_substlat,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k4_partfun1 @ A @ B ) ) & ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ),file(substlat,rc2_substlat)).
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(dt_c1_22__heyting2,axiom,( $true ),file(heyting2,c1_22__heyting2)).
thf(dt_c2_22__heyting2,axiom,( v1_finset_1 @ c2_22__heyting2 ),file(heyting2,c2_22__heyting2)).
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_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_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_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_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(fc10_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc10_relat_1)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_setwiseo,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) & ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ),file(setwiseo,rc1_setwiseo)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_setwiseo,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(setwiseo,rc2_setwiseo)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_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(rc8_pre_poly,axiom,( ? [A: $i] : ( ( v4_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(pre_poly,rc8_pre_poly)).
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_k4_partfun1,axiom,( $true ),file(partfun1,k4_partfun1)).
thf(dt_k5_finsub_1,axiom,( ! [A: $i] : ( v4_finsub_1 @ ( k5_finsub_1 @ A ) ) ),file(finsub_1,k5_finsub_1)).
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_c3_22__heyting2,axiom,( m1_subset_1 @ c3_22__heyting2 @ ( k5_finsub_1 @ ( k4_partfun1 @ c1_22__heyting2 @ c2_22__heyting2 ) ) ),file(heyting2,c3_22__heyting2)).
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(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(fc1_finset_1,axiom,( ! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ) ),file(finset_1,fc1_finset_1)).
thf(fc1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k4_partfun1 @ A @ B ) ) ),file(partfun1,fc1_partfun1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
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_xboole_0,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ) ),file(xboole_0,fc2_xboole_0)).
thf(fc30_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_tarski @ A ) ) ) ),file(finset_1,fc30_finset_1)).
thf(fc4_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( v4_funct_1 @ ( k4_partfun1 @ A @ B ) ) ),file(partfun1,fc4_partfun1)).
thf(e1_22__heyting2,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k4_partfun1 @ c3_22__heyting2 @ c3_22__heyting2 ) ) & ( = @ ( k9_xtuple_0 @ A ) @ c3_22__heyting2 ) ) ),file(heyting2,e1_22__heyting2)).
thf(s1_lattice3,axiom,( ! [A: $i] : ! [B: $i > $o] : ! [C: $i] : ( ? [D: $i] : ( ( m1_subset_1 @ D @ C ) & ( B @ D ) ) => ( = @ ( replSep1 @ ^ [D: $i] : ( m1_subset_1 @ D @ C ) @ ^ [D: $i] : A @ ^ [D: $i] : ( B @ D ) ) @ ( k1_tarski @ A ) ) ) ),file(lattice3,s1_lattice3)).
thf(e2_22__heyting2,conjecture,( = @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ ( k4_partfun1 @ c3_22__heyting2 @ c3_22__heyting2 ) ) @ ^ [A: $i] : k1_xboole_0 @ ^ [A: $i] : ( = @ ( k9_xtuple_0 @ A ) @ c3_22__heyting2 ) ) @ ( k1_tarski @ k1_xboole_0 ) ),file(heyting2,e2_22__heyting2)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
