% Mizar problem: e4_12,substlat,277,14 
include('Axioms/SET010^2.ax').
thf(c1_12_type,type,( c1_12__substlat: $i )).
thf(c2_12_type,type,( c2_12__substlat: $i )).
thf(c3_12_type,type,( c3_12__substlat: $i )).
thf(c4_12_type,type,( c4_12__substlat: $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k4_partfun1_type,type,( k4_partfun1: $i > $i > $i )).
thf(k5_finsub_1_type,type,( k5_finsub_1: $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(r1_partfun1_type,type,( r1_partfun1: $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_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(v3_finsub_1_type,type,( v3_finsub_1: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_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(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(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
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(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_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(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(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(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(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(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(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(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(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(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(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(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_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
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(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_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(symmetry_r1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( r1_partfun1 @ A @ B ) => ( r1_partfun1 @ B @ A ) ) ) ),file(partfun1,r1_partfun1)).
thf(reflexivity_r1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( r1_partfun1 @ A @ A ) ) ),file(partfun1,r1_partfun1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_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_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_12__substlat,axiom,( $true ),file(substlat,c1_12__substlat)).
thf(dt_c2_12__substlat,axiom,( $true ),file(substlat,c2_12__substlat)).
thf(dt_c3_12__substlat,axiom,( m1_subset_1 @ c3_12__substlat @ ( k5_finsub_1 @ ( k4_partfun1 @ c1_12__substlat @ c2_12__substlat ) ) ),file(substlat,c3_12__substlat)).
thf(dt_c4_12__substlat,axiom,( m1_subset_1 @ c4_12__substlat @ ( k5_finsub_1 @ ( k4_partfun1 @ c1_12__substlat @ c2_12__substlat ) ) ),file(substlat,c4_12__substlat)).
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(fc1_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k4_partfun1 @ A @ B ) ) ),file(partfun1,fc1_partfun1)).
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(fc4_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ( v4_funct_1 @ ( k4_partfun1 @ A @ B ) ) ),file(partfun1,fc4_partfun1)).
thf(e3_12__substlat,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k4_partfun1 @ c1_12__substlat @ c2_12__substlat ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k4_partfun1 @ c1_12__substlat @ c2_12__substlat ) ) => ( ( ( r2_hidden @ A @ c3_12__substlat ) & ( r2_hidden @ B @ c4_12__substlat ) & ( r1_partfun1 @ A @ B ) ) <=> ( ( r2_hidden @ B @ c4_12__substlat ) & ( r2_hidden @ A @ c3_12__substlat ) & ( r1_partfun1 @ B @ A ) ) ) ) ) ),file(substlat,e3_12__substlat)).
thf(e2_12__substlat,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k4_partfun1 @ c1_12__substlat @ c2_12__substlat ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k4_partfun1 @ c1_12__substlat @ c2_12__substlat ) ) => ( = @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ A ) ) ) ) ),file(substlat,e2_12__substlat)).
thf(s8_fraenkel,axiom,( ! [A: $i > $i > $i] : ! [B: $i > $i > $o] : ! [C: $i > $i > $o] : ! [D: $i] : ! [E: $i] : ( ( ! [F: $i] : ( ( m1_subset_1 @ F @ E ) => ! [G: $i] : ( ( m1_subset_1 @ G @ D ) => ( ( C @ F @ G ) <=> ( B @ F @ G ) ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ E ) => ! [G: $i] : ( ( m1_subset_1 @ G @ D ) => ( = @ ( A @ F @ G ) @ ( A @ G @ F ) ) ) ) ) => ( = @ ( replSep2 @ ^ [F: $i] : ( m1_subset_1 @ F @ E ) @ ^ [F: $i] : ^ [G: $i] : ( m1_subset_1 @ G @ D ) @ ^ [F: $i] : ^ [G: $i] : ( A @ F @ G ) @ ^ [F: $i] : ^ [G: $i] : ( C @ F @ G ) ) @ ( replSep2 @ ^ [F: $i] : ( m1_subset_1 @ F @ E ) @ ^ [F: $i] : ^ [G: $i] : ( m1_subset_1 @ G @ D ) @ ^ [F: $i] : ^ [G: $i] : ( A @ G @ F ) @ ^ [F: $i] : ^ [G: $i] : ( B @ F @ G ) ) ) ) ),file(fraenkel,s8_fraenkel)).
thf(e4_12__substlat,conjecture,( = @ ( replSep2 @ ^ [A: $i] : ( m1_subset_1 @ A @ ( k4_partfun1 @ c1_12__substlat @ c2_12__substlat ) ) @ ^ [A: $i] : ^ [B: $i] : ( m1_subset_1 @ B @ ( k4_partfun1 @ c1_12__substlat @ c2_12__substlat ) ) @ ^ [A: $i] : ^ [B: $i] : ( k2_xboole_0 @ A @ B ) @ ^ [A: $i] : ^ [B: $i] : ( ( r2_hidden @ A @ c3_12__substlat ) & ( r2_hidden @ B @ c4_12__substlat ) & ( r1_partfun1 @ A @ B ) ) ) @ ( replSep2 @ ^ [A: $i] : ( m1_subset_1 @ A @ ( k4_partfun1 @ c1_12__substlat @ c2_12__substlat ) ) @ ^ [A: $i] : ^ [B: $i] : ( m1_subset_1 @ B @ ( k4_partfun1 @ c1_12__substlat @ c2_12__substlat ) ) @ ^ [A: $i] : ^ [B: $i] : ( k2_xboole_0 @ B @ A ) @ ^ [A: $i] : ^ [B: $i] : ( ( r2_hidden @ B @ c4_12__substlat ) & ( r2_hidden @ A @ c3_12__substlat ) & ( r1_partfun1 @ B @ A ) ) ) ),file(substlat,e4_12__substlat)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
