% Mizar problem: e1_1_1_1,catalg_1,54,51 
include('Axioms/SET010^0.ax').
thf(c1_1_type,type,( c1_1__catalg_1: $i )).
thf(c2_1_type,type,( c2_1__catalg_1: $i )).
thf(c3_1_type,type,( c3_1__catalg_1: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k5_relat_1_type,type,( k5_relat_1: $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_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,k5_relat_1)).
thf(dt_c1_1__catalg_1,axiom,( $true ),file(catalg_1,c1_1__catalg_1)).
thf(dt_c2_1__catalg_1,axiom,( ( v1_relat_1 @ c2_1__catalg_1 ) & ( v1_funct_1 @ c2_1__catalg_1 ) ),file(catalg_1,c2_1__catalg_1)).
thf(dt_c3_1__catalg_1,axiom,( ( v1_relat_1 @ c3_1__catalg_1 ) & ( v1_funct_1 @ c3_1__catalg_1 ) ),file(catalg_1,c3_1__catalg_1)).
thf(fc27_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ C @ A ) ) & ( v4_relat_1 @ ( k5_relat_1 @ C @ A ) @ A ) & ( v4_relat_1 @ ( k5_relat_1 @ C @ A ) @ B ) ) ) ),file(relat_1,fc27_relat_1)).
thf(fc8_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(funct_1,fc8_funct_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(rd5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( = @ ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ B ) @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,rd5_relat_1)).
thf(rd8_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( = @ ( k5_relat_1 @ B @ A ) @ B ) ) ),file(relat_1,rd8_relat_1)).
thf(s4_pboole,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ),file(pboole,s4_pboole)).
thf(e1_1_1_1__catalg_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ c1_1__catalg_1 ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ c1_1__catalg_1 ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_1__catalg_1 ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k5_relat_1 @ c3_1__catalg_1 @ ( k1_funct_1 @ c2_1__catalg_1 @ B ) ) ) ) ) ),file(catalg_1,e1_1_1_1__catalg_1)).
