% Mizar problem: e3_20_1_1,projred1,993,54 
include('Axioms/SET010^0.ax').
thf(c1_20_type,type,( c1_20__projred1: $i )).
thf(c2_20_type,type,( c2_20__projred1: $i )).
thf(c3_20_type,type,( c3_20__projred1: $i )).
thf(c4_20_type,type,( c4_20__projred1: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_relset_1_type,type,( k1_relset_1: $i > $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $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(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_incproj_type,type,( v5_incproj: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $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(fc18_funct_1,axiom,( ! [A: $i] : ( ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(funct_1,fc18_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(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(cc9_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_funct_1 @ B ) ) ) ),file(funct_1,cc9_funct_1)).
thf(fc17_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v4_funct_1 @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ C @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ C @ B ) ) ) ) ),file(funct_1,fc17_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(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_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(cc3_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_funct_1 @ B ) ) ) ),file(funct_1,cc3_funct_1)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_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(cc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc7_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_1)).
thf(fc8_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) => ( v1_relat_1 @ ( k9_xtuple_0 @ D ) ) ) ),file(relset_1,fc8_relset_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relset_1,rc1_relset_1)).
thf(rc6_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) ) ),file(funct_1,rc6_funct_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( = @ ( k1_relset_1 @ A @ B ) @ ( k9_xtuple_0 @ B ) ) ) ),file(relset_1,k1_relset_1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( m1_subset_1 @ ( k1_relset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(relset_1,k1_relset_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
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_20__projred1,axiom,( ( v6_incsp_1 @ c1_20__projred1 ) & ( v1_incproj @ c1_20__projred1 ) & ( v2_incproj @ c1_20__projred1 ) & ( v3_incproj @ c1_20__projred1 ) & ( v4_incproj @ c1_20__projred1 ) & ( v5_incproj @ c1_20__projred1 ) & ( v9_incproj @ c1_20__projred1 ) & ( l1_incsp_1 @ c1_20__projred1 ) ),file(projred1,c1_20__projred1)).
thf(dt_c2_20__projred1,axiom,( m1_subset_1 @ c2_20__projred1 @ ( u2_incsp_1 @ c1_20__projred1 ) ),file(projred1,c2_20__projred1)).
thf(dt_c3_20__projred1,axiom,( m1_subset_1 @ c3_20__projred1 @ ( u2_incsp_1 @ c1_20__projred1 ) ),file(projred1,c3_20__projred1)).
thf(dt_c4_20__projred1,axiom,( m1_subset_1 @ c4_20__projred1 @ ( u1_incsp_1 @ c1_20__projred1 ) ),file(projred1,c4_20__projred1)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(e2_20_1_1__projred1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( r2_hidden @ A @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ? [C: $i] : ( ( m1_subset_1 @ C @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ( = @ C @ A ) & ( = @ D @ B ) & ( r1_incsp_1 @ c1_20__projred1 @ C @ c2_20__projred1 ) & ( r1_incsp_1 @ c1_20__projred1 @ D @ c3_20__projred1 ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( u2_incsp_1 @ c1_20__projred1 ) ) & ( r1_incsp_1 @ c1_20__projred1 @ c4_20__projred1 @ E ) & ( r1_incsp_1 @ c1_20__projred1 @ C @ E ) & ( r1_incsp_1 @ c1_20__projred1 @ D @ E ) ) ) ) ) => ( r2_hidden @ B @ ( u1_incsp_1 @ c1_20__projred1 ) ) ) ),file(projred1,e2_20_1_1__projred1)).
thf(e1_20_1_1__projred1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ( = @ D @ A ) & ( = @ E @ B ) & ( r1_incsp_1 @ c1_20__projred1 @ D @ c2_20__projred1 ) & ( r1_incsp_1 @ c1_20__projred1 @ E @ c3_20__projred1 ) & ? [F: $i] : ( ( m1_subset_1 @ F @ ( u2_incsp_1 @ c1_20__projred1 ) ) & ( r1_incsp_1 @ c1_20__projred1 @ c4_20__projred1 @ F ) & ( r1_incsp_1 @ c1_20__projred1 @ D @ F ) & ( r1_incsp_1 @ c1_20__projred1 @ E @ F ) ) ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ( = @ D @ A ) & ( = @ E @ C ) & ( r1_incsp_1 @ c1_20__projred1 @ D @ c2_20__projred1 ) & ( r1_incsp_1 @ c1_20__projred1 @ E @ c3_20__projred1 ) & ? [F: $i] : ( ( m1_subset_1 @ F @ ( u2_incsp_1 @ c1_20__projred1 ) ) & ( r1_incsp_1 @ c1_20__projred1 @ c4_20__projred1 @ F ) & ( r1_incsp_1 @ c1_20__projred1 @ D @ F ) & ( r1_incsp_1 @ c1_20__projred1 @ E @ F ) ) ) ) ) => ( = @ B @ C ) ) ),file(projred1,e1_20_1_1__projred1)).
thf(s2_partfun1,axiom,( ! [A: $i] : ! [B: $i > $i > $o] : ! [C: $i] : ( ( ! [D: $i] : ! [E: $i] : ( ( ( r2_hidden @ D @ C ) & ( B @ D @ E ) ) => ( r2_hidden @ E @ A ) ) & ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ( r2_hidden @ D @ C ) & ( B @ D @ E ) & ( B @ D @ F ) ) => ( = @ E @ F ) ) ) => ? [D: $i] : ( ( v1_funct_1 @ D ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ A ) ) ) & ! [E: $i] : ( ( r2_hidden @ E @ ( k1_relset_1 @ C @ D ) ) <=> ( ( r2_hidden @ E @ C ) & ? [F: $i] : ( B @ E @ F ) ) ) & ! [E: $i] : ( ( r2_hidden @ E @ ( k1_relset_1 @ C @ D ) ) => ( B @ E @ ( k1_funct_1 @ D @ E ) ) ) ) ) ),file(partfun1,s2_partfun1)).
thf(e3_20_1_1__projred1,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_incsp_1 @ c1_20__projred1 ) @ ( u1_incsp_1 @ c1_20__projred1 ) ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k1_relset_1 @ ( u1_incsp_1 @ c1_20__projred1 ) @ A ) ) <=> ( ( r2_hidden @ B @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ? [C: $i] : ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ( = @ D @ B ) & ( = @ E @ C ) & ( r1_incsp_1 @ c1_20__projred1 @ D @ c2_20__projred1 ) & ( r1_incsp_1 @ c1_20__projred1 @ E @ c3_20__projred1 ) & ? [F: $i] : ( ( m1_subset_1 @ F @ ( u2_incsp_1 @ c1_20__projred1 ) ) & ( r1_incsp_1 @ c1_20__projred1 @ c4_20__projred1 @ F ) & ( r1_incsp_1 @ c1_20__projred1 @ D @ F ) & ( r1_incsp_1 @ c1_20__projred1 @ E @ F ) ) ) ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k1_relset_1 @ ( u1_incsp_1 @ c1_20__projred1 ) @ A ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( u1_incsp_1 @ c1_20__projred1 ) ) & ( = @ C @ B ) & ( = @ D @ ( k1_funct_1 @ A @ B ) ) & ( r1_incsp_1 @ c1_20__projred1 @ C @ c2_20__projred1 ) & ( r1_incsp_1 @ c1_20__projred1 @ D @ c3_20__projred1 ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( u2_incsp_1 @ c1_20__projred1 ) ) & ( r1_incsp_1 @ c1_20__projred1 @ c4_20__projred1 @ E ) & ( r1_incsp_1 @ c1_20__projred1 @ C @ E ) & ( r1_incsp_1 @ c1_20__projred1 @ D @ E ) ) ) ) ) ) ),file(projred1,e3_20_1_1__projred1)).
