% Mizar problem: e2_30_1_1,pralg_1,1140,49 
include('Axioms/SET010^0.ax').
thf(c1_30_type,type,( c1_30__pralg_1: $i )).
thf(c2_30_type,type,( c2_30__pralg_1: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
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(v2_pralg_1_type,type,( v2_pralg_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_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_30__pralg_1,axiom,( $true ),file(pralg_1,c1_30__pralg_1)).
thf(dt_c2_30__pralg_1,axiom,( ( v1_relat_1 @ c2_30__pralg_1 ) & ( v4_relat_1 @ c2_30__pralg_1 @ c1_30__pralg_1 ) & ( v1_funct_1 @ c2_30__pralg_1 ) & ( v1_partfun1 @ c2_30__pralg_1 @ c1_30__pralg_1 ) & ( v2_pralg_1 @ c2_30__pralg_1 ) ),file(pralg_1,c2_30__pralg_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(rc3_pralg_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v2_pralg_1 @ B ) ) ),file(pralg_1,rc3_pralg_1)).
thf(e1_30_1_1__pralg_1,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ c1_30__pralg_1 ) & ! [B: $i] : ~ ( ? [C: $i] : ( ( l1_struct_0 @ C ) & ( = @ C @ ( k1_funct_1 @ c2_30__pralg_1 @ A ) ) & ( = @ B @ ( u1_struct_0 @ C ) ) ) ) ) ),file(pralg_1,e1_30_1_1__pralg_1)).
thf(s1_classes1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(classes1,s1_classes1)).
thf(e2_30_1_1__pralg_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ c1_30__pralg_1 ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_30__pralg_1 ) => ? [C: $i] : ( ( l1_struct_0 @ C ) & ( = @ C @ ( k1_funct_1 @ c2_30__pralg_1 @ B ) ) & ( = @ ( k1_funct_1 @ A @ B ) @ ( u1_struct_0 @ C ) ) ) ) ) ),file(pralg_1,e2_30_1_1__pralg_1)).
