% Mizar problem: e1_8_1,altcat_1,140,55 
include('Axioms/SET010^0.ax').
thf(f1_s3_altcat_1_type,type,( f1_s3_altcat_1: $i )).
thf(f2_s3_altcat_1_type,type,( f2_s3_altcat_1: $i )).
thf(f3_s3_altcat_1_type,type,( f3_s3_altcat_1: $i )).
thf(f4_s3_altcat_1_type,type,( f4_s3_altcat_1: $i > $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_xtuple_0_type,type,( k1_xtuple_0: $i > $i )).
thf(k2_xtuple_0_type,type,( k2_xtuple_0: $i > $i )).
thf(k3_zfmisc_1_type,type,( k3_zfmisc_1: $i > $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $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_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_xtuple_0,axiom,( $true ),file(xtuple_0,k1_xtuple_0)).
thf(dt_k2_xtuple_0,axiom,( $true ),file(xtuple_0,k2_xtuple_0)).
thf(dt_k3_zfmisc_1,axiom,( $true ),file(zfmisc_1,k3_zfmisc_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_f1_s3_altcat_1,axiom,( $true ),file(altcat_1,f1_s3_altcat_1)).
thf(dt_f2_s3_altcat_1,axiom,( $true ),file(altcat_1,f2_s3_altcat_1)).
thf(dt_f3_s3_altcat_1,axiom,( $true ),file(altcat_1,f3_s3_altcat_1)).
thf(dt_f4_s3_altcat_1,axiom,( $true ),file(altcat_1,f4_s3_altcat_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s3_funct_1,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ),file(funct_1,s3_funct_1)).
thf(e1_8_1__altcat_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k3_zfmisc_1 @ f1_s3_altcat_1 @ f2_s3_altcat_1 @ f3_s3_altcat_1 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k3_zfmisc_1 @ f1_s3_altcat_1 @ f2_s3_altcat_1 @ f3_s3_altcat_1 ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( f4_s3_altcat_1 @ ( k1_xtuple_0 @ ( k1_xtuple_0 @ B ) ) @ ( k2_xtuple_0 @ ( k1_xtuple_0 @ B ) ) @ ( k2_xtuple_0 @ B ) ) ) ) ) ),file(altcat_1,e1_8_1__altcat_1)).
