% Mizar problem: e9_28,projred1,1247,29 
include('Axioms/SET010^0.ax').
thf(c1_28_type,type,( c1_28__projred1: $i )).
thf(c5_28_type,type,( c5_28__projred1: $i )).
thf(u1_incsp_1_type,type,( u1_incsp_1: $i > $i )).
thf(u2_incsp_1_type,type,( u2_incsp_1: $i > $i )).
thf(l1_incsp_1_type,type,( l1_incsp_1: $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(r1_incsp_1_type,type,( r1_incsp_1: $i > $i > $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_incproj_type,type,( v1_incproj: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_incproj_type,type,( v2_incproj: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_incproj_type,type,( v3_incproj: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_incproj_type,type,( v4_incproj: $i > $o )).
thf(v5_incproj_type,type,( v5_incproj: $i > $o )).
thf(v6_incsp_1_type,type,( v6_incsp_1: $i > $o )).
thf(v9_incproj_type,type,( v9_incproj: $i > $o )).
thf(cc6_funct_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc6_funct_1)).
thf(cc5_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ) ),file(funct_1,cc5_funct_1)).
thf(rc2_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ),file(funct_1,rc2_funct_1)).
thf(rc5_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) ),file(funct_1,rc5_funct_1)).
thf(cc2_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ) ),file(funct_1,cc2_funct_1)).
thf(cc4_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc4_funct_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(cc8_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) ) ) ),file(funct_1,cc8_funct_1)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc7_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_l1_incsp_1,axiom,( $true ),file(incsp_1,l1_incsp_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_u1_incsp_1,axiom,( ! [A: $i] : ( ( l1_incsp_1 @ A ) => ~ ( v1_xboole_0 @ ( u1_incsp_1 @ A ) ) ) ),file(incsp_1,u1_incsp_1)).
thf(dt_u2_incsp_1,axiom,( ! [A: $i] : ( ( l1_incsp_1 @ A ) => ~ ( v1_xboole_0 @ ( u2_incsp_1 @ A ) ) ) ),file(incsp_1,u2_incsp_1)).
thf(dt_c1_28__projred1,axiom,( ( v6_incsp_1 @ c1_28__projred1 ) & ( v1_incproj @ c1_28__projred1 ) & ( v2_incproj @ c1_28__projred1 ) & ( v3_incproj @ c1_28__projred1 ) & ( v4_incproj @ c1_28__projred1 ) & ( v5_incproj @ c1_28__projred1 ) & ( v9_incproj @ c1_28__projred1 ) & ( l1_incsp_1 @ c1_28__projred1 ) ),file(projred1,c1_28__projred1)).
thf(dt_c5_28__projred1,axiom,( m1_subset_1 @ c5_28__projred1 @ ( u2_incsp_1 @ c1_28__projred1 ) ),file(projred1,c5_28__projred1)).
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(e9_28__projred1,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ ( u1_incsp_1 @ c1_28__projred1 ) ) & ? [C: $i] : ( ( m1_subset_1 @ C @ ( u1_incsp_1 @ c1_28__projred1 ) ) & ( = @ B @ C ) & ( r1_incsp_1 @ c1_28__projred1 @ C @ c5_28__projred1 ) ) ) ) ),file(projred1,e9_28__projred1)).
