% Mizar problem: e1_3,bvfunc_2,75,6 
include('Axioms/SET010^0.ax').
thf(c1_3_type,type,( c1_3__bvfunc_2: $i )).
thf(c2_3_type,type,( c2_3__bvfunc_2: $i )).
thf(c3_3_type,type,( c3_3__bvfunc_2: $i )).
thf(k11_eqrel_1_type,type,( k11_eqrel_1: $i > $i > $i > $i )).
thf(k15_bvfunc_1_type,type,( k15_bvfunc_1: $i > $i > $i > $i )).
thf(k1_bvfunc_2_type,type,( k1_bvfunc_2: $i > $i )).
thf(k1_partit1_type,type,( k1_partit1: $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(k7_partfun1_type,type,( k7_partfun1: $i > $i > $i > $i )).
thf(k9_setfam_1_type,type,( k9_setfam_1: $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(m1_bvfunc_1_type,type,( m1_bvfunc_1: $i > $i > $i > $o )).
thf(m1_bvfunc_2_type,type,( m1_bvfunc_2: $i > $i > $i > $o )).
thf(m1_eqrel_1_type,type,( m1_eqrel_1: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(v1_eqrel_1_type,type,( v1_eqrel_1: $i > $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_setfam_1_type,type,( v1_setfam_1: $i > $o )).
thf(v1_subset_1_type,type,( v1_subset_1: $i > $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v2_card_3_type,type,( v2_card_3: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(rc2_eqrel_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_eqrel_1 @ B @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_setfam_1 @ B ) ) ) ),file(eqrel_1,rc2_eqrel_1)).
thf(rc4_eqrel_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_eqrel_1 @ B @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_setfam_1 @ B ) ) ) ),file(eqrel_1,rc4_eqrel_1)).
thf(redefinition_m1_bvfunc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_eqrel_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_bvfunc_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(bvfunc_1,m1_bvfunc_1)).
thf(dt_k11_eqrel_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) & ( m1_eqrel_1 @ C @ A ) ) => ( m1_subset_1 @ ( k11_eqrel_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(eqrel_1,k11_eqrel_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_m1_bvfunc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_eqrel_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_bvfunc_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ) ),file(bvfunc_1,m1_bvfunc_1)).
thf(dt_m1_eqrel_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_eqrel_1 @ B @ A ) => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),file(eqrel_1,m1_eqrel_1)).
thf(cc1_eqrel_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_eqrel_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ),file(eqrel_1,cc1_eqrel_1)).
thf(cc2_eqrel_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_eqrel_1 @ B @ A ) => ( v1_setfam_1 @ B ) ) ),file(eqrel_1,cc2_eqrel_1)).
thf(cc2_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ~ ( v1_subset_1 @ B @ A ) => ~ ( v1_xboole_0 @ B ) ) ) ) ),file(subset_1,cc2_subset_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_eqrel_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k9_setfam_1 @ A ) ) ) ) & ( v1_eqrel_1 @ B @ A ) ) ),file(eqrel_1,rc1_eqrel_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(rc3_eqrel_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k9_setfam_1 @ A ) ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_eqrel_1 @ B @ A ) ) ),file(eqrel_1,rc3_eqrel_1)).
thf(rc3_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_subset_1 @ B @ A ) ) ),file(subset_1,rc3_subset_1)).
thf(rc4_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,rc4_subset_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k15_bvfunc_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) & ( m1_eqrel_1 @ C @ A ) ) => ( = @ ( k15_bvfunc_1 @ A @ B @ C ) @ ( k11_eqrel_1 @ A @ B @ C ) ) ) ),file(bvfunc_1,k15_bvfunc_1)).
thf(redefinition_k1_bvfunc_2,axiom,( ! [A: $i] : ( = @ ( k1_bvfunc_2 @ A ) @ ( k1_partit1 @ A ) ) ),file(bvfunc_2,k1_bvfunc_2)).
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(redefinition_k9_setfam_1,axiom,( ! [A: $i] : ( = @ ( k9_setfam_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),file(setfam_1,k9_setfam_1)).
thf(redefinition_m1_bvfunc_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v1_eqrel_1 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k9_setfam_1 @ A ) ) ) ) ) => ! [C: $i] : ( ( m1_bvfunc_2 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(bvfunc_2,m1_bvfunc_2)).
thf(dt_k15_bvfunc_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) & ( m1_eqrel_1 @ C @ A ) ) => ( m1_bvfunc_1 @ ( k15_bvfunc_1 @ A @ B @ C ) @ A @ C ) ) ),file(bvfunc_1,k15_bvfunc_1)).
thf(dt_k1_bvfunc_2,axiom,( ! [A: $i] : ( ( v1_eqrel_1 @ ( k1_bvfunc_2 @ A ) @ A ) & ( m1_subset_1 @ ( k1_bvfunc_2 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k9_setfam_1 @ A ) ) ) ) ) ),file(bvfunc_2,k1_bvfunc_2)).
thf(dt_k1_partit1,axiom,( $true ),file(partit1,k1_partit1)).
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_k7_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( m1_subset_1 @ ( k7_partfun1 @ A @ B @ C ) @ A ) ) ),file(partfun1,k7_partfun1)).
thf(dt_k9_setfam_1,axiom,( ! [A: $i] : ( m1_subset_1 @ ( k9_setfam_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(setfam_1,k9_setfam_1)).
thf(dt_m1_bvfunc_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( v1_eqrel_1 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k9_setfam_1 @ A ) ) ) ) ) => ! [C: $i] : ( ( m1_bvfunc_2 @ C @ A @ B ) => ( m1_eqrel_1 @ C @ A ) ) ) ),file(bvfunc_2,m1_bvfunc_2)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_3__bvfunc_2,axiom,( ~ ( v1_xboole_0 @ c1_3__bvfunc_2 ) ),file(bvfunc_2,c1_3__bvfunc_2)).
thf(dt_c2_3__bvfunc_2,axiom,( m1_subset_1 @ c2_3__bvfunc_2 @ ( k1_zfmisc_1 @ ( k1_partit1 @ c1_3__bvfunc_2 ) ) ),file(bvfunc_2,c2_3__bvfunc_2)).
thf(dt_c3_3__bvfunc_2,axiom,( m1_subset_1 @ c3_3__bvfunc_2 @ c1_3__bvfunc_2 ),file(bvfunc_2,c3_3__bvfunc_2)).
thf(cc1_margrel1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v2_card_3 @ A ) ) ),file(margrel1,cc1_margrel1)).
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(cc1_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_xboole_0 @ B ) ) ) ),file(subset_1,cc1_subset_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(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(cc3_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ( v1_xboole_0 @ B ) => ( v1_subset_1 @ B @ A ) ) ) ) ),file(subset_1,cc3_subset_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(cc4_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ~ ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,cc4_subset_1)).
thf(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(fc1_partit1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_partit1 @ A ) ) ),file(partit1,fc1_partit1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(rc1_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(subset_1,rc1_subset_1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_xboole_0 @ B ) ) ),file(subset_1,rc2_subset_1)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(s2_partfun2,axiom,( ! [A: $i > $i] : ! [B: $i > $o] : ! [C: $i] : ! [D: $i] : ? [E: $i] : ( ( v1_funct_1 @ E ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ D @ C ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ( ( r2_hidden @ F @ ( k1_relset_1 @ D @ E ) ) <=> ( B @ F ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ( ( r2_hidden @ F @ ( k1_relset_1 @ D @ E ) ) => ( = @ ( k7_partfun1 @ C @ E @ F ) @ ( A @ F ) ) ) ) ) ),file(partfun2,s2_partfun2)).
thf(e1_3__bvfunc_2,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k1_bvfunc_2 @ c1_3__bvfunc_2 ) @ ( k9_setfam_1 @ c1_3__bvfunc_2 ) ) ) ) & ! [B: $i] : ( ( m1_bvfunc_2 @ B @ c1_3__bvfunc_2 @ ( k1_bvfunc_2 @ c1_3__bvfunc_2 ) ) => ( ( r2_hidden @ B @ ( k1_relset_1 @ ( k1_bvfunc_2 @ c1_3__bvfunc_2 ) @ A ) ) <=> ( r2_hidden @ B @ c2_3__bvfunc_2 ) ) ) & ! [B: $i] : ( ( m1_bvfunc_2 @ B @ c1_3__bvfunc_2 @ ( k1_bvfunc_2 @ c1_3__bvfunc_2 ) ) => ( ( r2_hidden @ B @ ( k1_relset_1 @ ( k1_bvfunc_2 @ c1_3__bvfunc_2 ) @ A ) ) => ( = @ ( k7_partfun1 @ ( k9_setfam_1 @ c1_3__bvfunc_2 ) @ A @ B ) @ ( k15_bvfunc_1 @ c1_3__bvfunc_2 @ c3_3__bvfunc_2 @ B ) ) ) ) ) ),file(bvfunc_2,e1_3__bvfunc_2)).
