% Mizar problem: e1_19_1_1,setfam_1,363,8 
include('Axioms/SET010^0.ax').
thf(c1_19_type,type,( c1_19__setfam_1: $i )).
thf(c2_19_type,type,( c2_19__setfam_1: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k3_tarski_type,type,( k3_tarski: $i > $i )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
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(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(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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
thf(dt_k3_tarski,axiom,( $true ),file(tarski,k3_tarski)).
thf(dt_c1_19__setfam_1,axiom,( $true ),file(setfam_1,c1_19__setfam_1)).
thf(dt_c2_19__setfam_1,axiom,( $true ),file(setfam_1,c2_19__setfam_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(s1_xboole_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ? [C: $i] : ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( r2_hidden @ D @ B ) & ( A @ D ) ) ) ),file(xboole_0,s1_xboole_0)).
thf(e1_19_1_1__setfam_1,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ ( k3_tarski @ c1_19__setfam_1 ) @ ( k3_tarski @ c2_19__setfam_1 ) ) ) ) & ? [C: $i] : ( ( = @ B @ C ) & ? [D: $i] : ? [E: $i] : ( ( r2_hidden @ D @ c1_19__setfam_1 ) & ( r2_hidden @ E @ c2_19__setfam_1 ) & ( = @ C @ ( k2_xboole_0 @ D @ E ) ) ) ) ) ) ),file(setfam_1,e1_19_1_1__setfam_1)).
