% Mizar problem: e5_74,closure1,1726,14 
include('Axioms/SET010^0.ax').
thf(c1_74_type,type,( c1_74__closure1: $i )).
thf(c2_74_type,type,( c2_74__closure1: $i )).
thf(c3_74_type,type,( c3_74__closure1: $i )).
thf(c4_74_type,type,( c4_74__closure1: $i )).
thf(c6_74_type,type,( c6_74__closure1: $i )).
thf(k1_mboolean_type,type,( k1_mboolean: $i > $i > $i )).
thf(k5_mssubfam_type,type,( k5_mssubfam: $i > $i > $i )).
thf(m1_pboole_type,type,( m1_pboole: $i > $i > $i > $o )).
thf(m3_pboole_type,type,( m3_pboole: $i > $i > $i > $o )).
thf(r1_pboole_type,type,( r1_pboole: $i > $i > $i > $o )).
thf(r2_pboole_type,type,( r2_pboole: $i > $i > $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_mssubfam_type,type,( v1_mssubfam: $i > $i > $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_mssubfam_type,type,( v2_mssubfam: $i > $i > $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v3_mssubfam_type,type,( v3_mssubfam: $i > $i > $i > $o )).
thf(v4_mssubfam_type,type,( v4_mssubfam: $i > $i > $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_mssubfam_type,type,( v5_mssubfam: $i > $i > $i > $o )).
thf(v6_mssubfam_type,type,( v6_mssubfam: $i > $i > $i > $o )).
thf(dt_c2_74__closure1,axiom,( ( v1_relat_1 @ c2_74__closure1 ) & ( v4_relat_1 @ c2_74__closure1 @ c1_74__closure1 ) & ( v1_funct_1 @ c2_74__closure1 ) & ( v1_partfun1 @ c2_74__closure1 @ c1_74__closure1 ) ),file(closure1,c2_74__closure1)).
thf(cc3_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 ) ) => ( ( v2_mssubfam @ C @ A @ B ) => ( v1_mssubfam @ C @ A @ B ) ) ) ) ),file(mssubfam,cc3_mssubfam)).
thf(cc6_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 ) ) => ( ( v5_mssubfam @ C @ A @ B ) => ( v2_relat_1 @ C ) ) ) ) ),file(mssubfam,cc6_mssubfam)).
thf(cc7_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 ) ) => ( ( v2_mssubfam @ C @ A @ B ) => ( v6_mssubfam @ C @ A @ B ) ) ) ) ),file(mssubfam,cc7_mssubfam)).
thf(cc8_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 ) ) => ( ( v6_mssubfam @ C @ A @ B ) => ( v2_relat_1 @ C ) ) ) ) ),file(mssubfam,cc8_mssubfam)).
thf(rc5_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 ) & ( v1_mssubfam @ C @ A @ B ) & ( v2_mssubfam @ C @ A @ B ) & ( v3_mssubfam @ C @ A @ B ) & ( v4_mssubfam @ C @ A @ B ) & ( v5_mssubfam @ C @ A @ B ) & ( v6_mssubfam @ C @ A @ B ) ) ) ),file(mssubfam,rc5_mssubfam)).
thf(reflexivity_r2_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( r2_pboole @ A @ B @ B ) ) ),file(pboole,r2_pboole)).
thf(redefinition_k5_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( = @ ( k5_mssubfam @ A @ B ) @ ( k1_mboolean @ A @ B ) ) ) ),file(mssubfam,k5_mssubfam)).
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_k5_mssubfam,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( ( v1_mssubfam @ ( k5_mssubfam @ A @ B ) @ A @ B ) & ( v2_mssubfam @ ( k5_mssubfam @ A @ B ) @ A @ B ) & ( v3_mssubfam @ ( k5_mssubfam @ A @ B ) @ A @ B ) & ( v4_mssubfam @ ( k5_mssubfam @ A @ B ) @ A @ B ) & ( v5_mssubfam @ ( k5_mssubfam @ A @ B ) @ A @ B ) & ( v6_mssubfam @ ( k5_mssubfam @ A @ B ) @ A @ B ) & ( m3_pboole @ ( k5_mssubfam @ A @ B ) @ A @ ( k1_mboolean @ A @ B ) ) ) ) ),file(mssubfam,k5_mssubfam)).
thf(dt_m1_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] : ( ( m1_pboole @ C @ A @ B ) => ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) ) ) ),file(pboole,m1_pboole)).
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_74__closure1,axiom,( $true ),file(closure1,c1_74__closure1)).
thf(dt_c3_74__closure1,axiom,( ( v4_mssubfam @ c3_74__closure1 @ c1_74__closure1 @ c2_74__closure1 ) & ( m3_pboole @ c3_74__closure1 @ c1_74__closure1 @ ( k1_mboolean @ c1_74__closure1 @ c2_74__closure1 ) ) ),file(closure1,c3_74__closure1)).
thf(dt_c4_74__closure1,axiom,( m1_pboole @ c4_74__closure1 @ c1_74__closure1 @ ( k5_mssubfam @ c1_74__closure1 @ c2_74__closure1 ) ),file(closure1,c4_74__closure1)).
thf(dt_c6_74__closure1,axiom,( ( v2_relat_1 @ c6_74__closure1 ) & ( m3_pboole @ c6_74__closure1 @ c1_74__closure1 @ ( k1_mboolean @ c1_74__closure1 @ c2_74__closure1 ) ) ),file(closure1,c6_74__closure1)).
thf(cc4_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 ) ) => ( ( v4_mssubfam @ C @ A @ B ) => ( v3_mssubfam @ C @ A @ B ) ) ) ) ),file(mssubfam,cc4_mssubfam)).
thf(cc5_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 ) ) => ( ( v4_mssubfam @ C @ A @ B ) => ( v5_mssubfam @ C @ A @ B ) ) ) ) ),file(mssubfam,cc5_mssubfam)).
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(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(s1_closure1,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v2_relat_1 @ D ) & ( v4_relat_1 @ D @ C ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ C ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ C ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ C ) ) => ( ! [E: $i] : ( ( ( v1_relat_1 @ E ) & ( v4_relat_1 @ E @ C ) & ( v1_funct_1 @ E ) & ( v1_partfun1 @ E @ C ) ) => ( ( r1_pboole @ C @ E @ D ) <=> ( ( r1_pboole @ C @ E @ B ) & ( A @ E ) ) ) ) => ( r2_pboole @ C @ D @ B ) ) ) ),file(closure1,s1_closure1)).
thf(e5_74__closure1,conjecture,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ c1_74__closure1 ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ c1_74__closure1 ) ) => ( ( r1_pboole @ c1_74__closure1 @ A @ c6_74__closure1 ) <=> ( ( r1_pboole @ c1_74__closure1 @ A @ c3_74__closure1 ) & ( r2_pboole @ c1_74__closure1 @ c4_74__closure1 @ A ) ) ) ) => ( r2_pboole @ c1_74__closure1 @ c6_74__closure1 @ c3_74__closure1 ) ),file(closure1,e5_74__closure1)).
