% Mizar problem: e1_3_1_1,msafree,157,60 
include('Axioms/SET010^0.ax').
thf(c1_3_type,type,( c1_3__msafree: $i )).
thf(c2_3_type,type,( c2_3__msafree: $i )).
thf(c3_3_type,type,( c3_3__msafree: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(v1_funct_1_type,type,( v1_funct_1: $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_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_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_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_c1_3__msafree,axiom,( $true ),file(msafree,c1_3__msafree)).
thf(dt_c2_3__msafree,axiom,( ( v1_relat_1 @ c2_3__msafree ) & ( v4_relat_1 @ c2_3__msafree @ c1_3__msafree ) & ( v1_funct_1 @ c2_3__msafree ) & ( v1_partfun1 @ c2_3__msafree @ c1_3__msafree ) ),file(msafree,c2_3__msafree)).
thf(dt_c3_3__msafree,axiom,( $true ),file(msafree,c3_3__msafree)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_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_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc1_pboole)).
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_3_1_1__msafree,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ ( k1_funct_1 @ c2_3__msafree @ c3_3__msafree ) @ c1_3__msafree ) ) & ? [C: $i] : ( ( r2_hidden @ C @ ( k1_funct_1 @ c2_3__msafree @ c3_3__msafree ) ) & ( = @ B @ ( k4_tarski @ C @ c3_3__msafree ) ) ) ) ) ),file(msafree,e1_3_1_1__msafree)).
