% Mizar problem: e6_20,substlat,418,19 
include('Axioms/SET010^0.ax').
thf(c1_20_type,type,( c1_20__substlat: $i )).
thf(c2_20_type,type,( c2_20__substlat: $i )).
thf(c3_20_type,type,( c3_20__substlat: $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_tarski_type,type,( r1_tarski: $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(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(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(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(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_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(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(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(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_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(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(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(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(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_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(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
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_20__substlat,axiom,( $true ),file(substlat,c1_20__substlat)).
thf(dt_c2_20__substlat,axiom,( $true ),file(substlat,c2_20__substlat)).
thf(dt_c3_20__substlat,axiom,( m1_subset_1 @ c3_20__substlat @ ( k5_finsub_1 @ ( k4_partfun1 @ c1_20__substlat @ c2_20__substlat ) ) ),file(substlat,c3_20__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(e5_20__substlat,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k4_partfun1 @ c1_20__substlat @ c2_20__substlat ) ) => ( r1_tarski @ A @ A ) ) ),file(substlat,e5_20__substlat)).
thf(e4_20__substlat,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k4_partfun1 @ c1_20__substlat @ c2_20__substlat ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k4_partfun1 @ c1_20__substlat @ c2_20__substlat ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k4_partfun1 @ c1_20__substlat @ c2_20__substlat ) ) => ( ( ( r1_tarski @ A @ B ) & ( r1_tarski @ B @ C ) ) => ( r1_tarski @ A @ C ) ) ) ) ) ),file(substlat,e4_20__substlat)).
thf(s23_fraenkel,axiom,( ! [A: $i] : ! [B: $i > $i > $o] : ! [C: $i] : ( ( ! [D: $i] : ( ( m1_subset_1 @ D @ C ) => ( B @ D @ D ) ) & ! [D: $i] : ( ( m1_subset_1 @ D @ C ) => ! [E: $i] : ( ( m1_subset_1 @ E @ C ) => ! [F: $i] : ( ( m1_subset_1 @ F @ C ) => ( ( ( B @ D @ E ) & ( B @ E @ F ) ) => ( B @ D @ F ) ) ) ) ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ C ) => ~ ( ( r2_hidden @ D @ A ) & ! [E: $i] : ( ( m1_subset_1 @ E @ C ) => ~ ( ( r2_hidden @ E @ A ) & ( B @ E @ D ) & ! [F: $i] : ( ( m1_subset_1 @ F @ C ) => ( ( ( r2_hidden @ F @ A ) & ( B @ F @ E ) ) => ( B @ E @ F ) ) ) ) ) ) ) ) ),file(fraenkel,s23_fraenkel)).
thf(e6_20__substlat,conjecture,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k4_partfun1 @ c1_20__substlat @ c2_20__substlat ) ) => ~ ( ( r2_hidden @ A @ c3_20__substlat ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( k4_partfun1 @ c1_20__substlat @ c2_20__substlat ) ) => ~ ( ( r2_hidden @ B @ c3_20__substlat ) & ( r1_tarski @ B @ A ) & ! [C: $i] : ( ( m1_subset_1 @ C @ ( k4_partfun1 @ c1_20__substlat @ c2_20__substlat ) ) => ( ( ( r2_hidden @ C @ c3_20__substlat ) & ( r1_tarski @ C @ B ) ) => ( r1_tarski @ B @ C ) ) ) ) ) ) ) ),file(substlat,e6_20__substlat)).
