% Mizar problem: e1_19_2_1,altcat_1,304,44 
include('Axioms/SET010^0.ax').
thf(c1_19_type,type,( c1_19__altcat_1: $i )).
thf(c2_19_type,type,( c2_19__altcat_1: $i )).
thf(c3_19_type,type,( c3_19__altcat_1: $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_multop_1_type,type,( k1_multop_1: $i > $i > $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_zfmisc_1_type,type,( k3_zfmisc_1: $i > $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(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k1_multop_1,axiom,( $true ),file(multop_1,k1_multop_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_zfmisc_1,axiom,( $true ),file(zfmisc_1,k3_zfmisc_1)).
thf(dt_c1_19__altcat_1,axiom,( $true ),file(altcat_1,c1_19__altcat_1)).
thf(dt_c2_19__altcat_1,axiom,( ( v1_relat_1 @ c2_19__altcat_1 ) & ( v4_relat_1 @ c2_19__altcat_1 @ ( k2_zfmisc_1 @ c1_19__altcat_1 @ c1_19__altcat_1 ) ) & ( v1_funct_1 @ c2_19__altcat_1 ) & ( v1_partfun1 @ c2_19__altcat_1 @ ( k2_zfmisc_1 @ c1_19__altcat_1 @ c1_19__altcat_1 ) ) ),file(altcat_1,c2_19__altcat_1)).
thf(dt_c3_19__altcat_1,axiom,( ( v1_relat_1 @ c3_19__altcat_1 ) & ( v4_relat_1 @ c3_19__altcat_1 @ ( k2_zfmisc_1 @ c1_19__altcat_1 @ c1_19__altcat_1 ) ) & ( v1_funct_1 @ c3_19__altcat_1 ) & ( v1_partfun1 @ c3_19__altcat_1 @ ( k2_zfmisc_1 @ c1_19__altcat_1 @ c1_19__altcat_1 ) ) ),file(altcat_1,c3_19__altcat_1)).
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(s3_altcat_1,axiom,( ! [A: $i > $i > $i > $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ? [E: $i] : ( ( v1_relat_1 @ E ) & ( v4_relat_1 @ E @ ( k3_zfmisc_1 @ D @ C @ B ) ) & ( v1_funct_1 @ E ) & ( v1_partfun1 @ E @ ( k3_zfmisc_1 @ D @ C @ B ) ) & ! [F: $i] : ! [G: $i] : ! [H: $i] : ( ( ( r2_hidden @ F @ D ) & ( r2_hidden @ G @ C ) & ( r2_hidden @ H @ B ) ) => ( = @ ( k1_multop_1 @ E @ F @ G @ H ) @ ( A @ F @ G @ H ) ) ) ) ),file(altcat_1,s3_altcat_1)).
thf(e1_19_2_1__altcat_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ ( k3_zfmisc_1 @ c1_19__altcat_1 @ c1_19__altcat_1 @ c1_19__altcat_1 ) ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ ( k3_zfmisc_1 @ c1_19__altcat_1 @ c1_19__altcat_1 @ c1_19__altcat_1 ) ) & ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( r2_hidden @ B @ c1_19__altcat_1 ) & ( r2_hidden @ C @ c1_19__altcat_1 ) & ( r2_hidden @ D @ c1_19__altcat_1 ) ) => ( = @ ( k1_multop_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k1_binop_1 @ c3_19__altcat_1 @ C @ D ) @ ( k1_binop_1 @ c2_19__altcat_1 @ B @ C ) ) ) ) ) ),file(altcat_1,e1_19_2_1__altcat_1)).
