% Mizar problem: e2_63_1_1,mssubfam,1262,8 
include('Axioms/SET010^0.ax').
thf(c1_63_type,type,( c1_63__mssubfam: $i )).
thf(c2_63_type,type,( c2_63__mssubfam: $i )).
thf(c3_63_type,type,( c3_63__mssubfam: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_mboolean_type,type,( k1_mboolean: $i > $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k8_setfam_1_type,type,( k8_setfam_1: $i > $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m3_pboole_type,type,( m3_pboole: $i > $i > $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_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(rc2_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m3_pboole @ C @ A @ ( k1_mboolean @ A @ B ) ) & ( v1_relat_1 @ C ) & ( v2_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) ) ),file(mssubfam,rc2_mssubfam)).
thf(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc3_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc3_funct_1)).
thf(rc3_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc3_pboole)).
thf(rc4_funcop_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(funcop_1,rc4_funcop_1)).
thf(rc5_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ? [C: $i] : ( ( m3_pboole @ C @ A @ B ) & ( v1_relat_1 @ C ) & ( v2_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) ) ),file(pboole,rc5_pboole)).
thf(rc9_funct_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) ),file(funct_1,rc9_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_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_mboolean,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ ( k1_mboolean @ A @ B ) ) & ( v4_relat_1 @ ( k1_mboolean @ A @ B ) @ A ) & ( v1_funct_1 @ ( k1_mboolean @ A @ B ) ) & ( v1_partfun1 @ ( k1_mboolean @ A @ B ) @ A ) ) ) ),file(mboolean,k1_mboolean)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k8_setfam_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(setfam_1,k8_setfam_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ! [C: $i] : ( ( m3_pboole @ C @ A @ B ) => ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) ) ) ),file(pboole,m3_pboole)).
thf(dt_c1_63__mssubfam,axiom,( $true ),file(mssubfam,c1_63__mssubfam)).
thf(dt_c2_63__mssubfam,axiom,( ( v1_relat_1 @ c2_63__mssubfam ) & ( v4_relat_1 @ c2_63__mssubfam @ c1_63__mssubfam ) & ( v1_funct_1 @ c2_63__mssubfam ) & ( v1_partfun1 @ c2_63__mssubfam @ c1_63__mssubfam ) ),file(mssubfam,c2_63__mssubfam)).
thf(dt_c3_63__mssubfam,axiom,( m3_pboole @ c3_63__mssubfam @ c1_63__mssubfam @ ( k1_mboolean @ c1_63__mssubfam @ c2_63__mssubfam ) ),file(mssubfam,c3_63__mssubfam)).
thf(cc2_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_relat_1 @ B ) ) ) ),file(relat_1,cc2_relat_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(cc5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v4_relat_1 @ C @ A ) ) ) ),file(relat_1,cc5_relat_1)).
thf(fc1_mboolean,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_relat_1 @ ( k1_mboolean @ A @ B ) ) & ( v2_relat_1 @ ( k1_mboolean @ A @ B ) ) & ( v4_relat_1 @ ( k1_mboolean @ A @ B ) @ A ) & ( v1_funct_1 @ ( k1_mboolean @ A @ B ) ) & ( v1_partfun1 @ ( k1_mboolean @ A @ B ) @ A ) ) ) ),file(mboolean,fc1_mboolean)).
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(e1_63_1_1__mssubfam,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ c1_63__mssubfam ) & ! [B: $i] : ~ ( ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_funct_1 @ c2_63__mssubfam @ A ) ) ) ) & ( = @ C @ ( k1_funct_1 @ c3_63__mssubfam @ A ) ) & ( = @ B @ ( k8_setfam_1 @ ( k1_funct_1 @ c2_63__mssubfam @ A ) @ C ) ) ) ) ) ),file(mssubfam,e1_63_1_1__mssubfam)).
thf(s3_pboole,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) => ? [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 ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(pboole,s3_pboole)).
thf(e2_63_1_1__mssubfam,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ c1_63__mssubfam ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ c1_63__mssubfam ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_63__mssubfam ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_funct_1 @ c2_63__mssubfam @ B ) ) ) ) & ( = @ C @ ( k1_funct_1 @ c3_63__mssubfam @ B ) ) & ( = @ ( k1_funct_1 @ A @ B ) @ ( k8_setfam_1 @ ( k1_funct_1 @ c2_63__mssubfam @ B ) @ C ) ) ) ) ) ),file(mssubfam,e2_63_1_1__mssubfam)).
