% Mizar problem: e20_82_1,closure1,2080,24 
include('Axioms/SET010^0.ax').
thf(c1_82_type,type,( c1_82__closure1: $i )).
thf(c2_82_type,type,( c2_82__closure1: $i )).
thf(c6_82_1_type,type,( c6_82_1__closure1: $i )).
thf(c7_82_1_type,type,( c7_82_1__closure1: $i )).
thf(k1_mboolean_type,type,( k1_mboolean: $i > $i > $i )).
thf(k5_mssubfam_type,type,( k5_mssubfam: $i > $i > $i )).
thf(u1_closure1_type,type,( u1_closure1: $i > $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u3_msualg_1_type,type,( u3_msualg_1: $i > $i > $i )).
thf(l1_closure1_type,type,( l1_closure1: $i > $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l2_msualg_1_type,type,( l2_msualg_1: $i > $i > $o )).
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(v10_closure1_type,type,( v10_closure1: $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(v8_closure1_type,type,( v8_closure1: $i > $i > $o )).
thf(v9_closure1_type,type,( v9_closure1: $i > $i > $o )).
thf(dt_l2_msualg_1,axiom,( $true ),file(msualg_1,l2_msualg_1)).
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(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(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(fc6_closure1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_struct_0 @ A ) & ( v8_closure1 @ B @ A ) & ( l1_closure1 @ B @ A ) ) => ( v3_mssubfam @ ( u1_closure1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) ),file(closure1,fc6_closure1)).
thf(fc8_closure1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_struct_0 @ A ) & ( v10_closure1 @ B @ A ) & ( l1_closure1 @ B @ A ) ) => ( v5_mssubfam @ ( u1_closure1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) ),file(closure1,fc8_closure1)).
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_l1_closure1,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ! [B: $i] : ( ( l1_closure1 @ B @ A ) => ( l2_msualg_1 @ B @ A ) ) ) ),file(closure1,l1_closure1)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
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_u1_closure1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_struct_0 @ A ) & ( l1_closure1 @ B @ A ) ) => ( m3_pboole @ ( u1_closure1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( k1_mboolean @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) ) ),file(closure1,u1_closure1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_u3_msualg_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_struct_0 @ A ) & ( l2_msualg_1 @ B @ A ) ) => ( ( v1_relat_1 @ ( u3_msualg_1 @ A @ B ) ) & ( v4_relat_1 @ ( u3_msualg_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) & ( v1_funct_1 @ ( u3_msualg_1 @ A @ B ) ) & ( v1_partfun1 @ ( u3_msualg_1 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),file(msualg_1,u3_msualg_1)).
thf(dt_c1_82__closure1,axiom,( l1_struct_0 @ c1_82__closure1 ),file(closure1,c1_82__closure1)).
thf(dt_c2_82__closure1,axiom,( ( v9_closure1 @ c2_82__closure1 @ c1_82__closure1 ) & ( l1_closure1 @ c2_82__closure1 @ c1_82__closure1 ) ),file(closure1,c2_82__closure1)).
thf(dt_c6_82_1__closure1,axiom,( m1_pboole @ c6_82_1__closure1 @ ( u1_struct_0 @ c1_82__closure1 ) @ ( k5_mssubfam @ ( u1_struct_0 @ c1_82__closure1 ) @ ( u3_msualg_1 @ c1_82__closure1 @ c2_82__closure1 ) ) ),file(closure1,c6_82_1__closure1)).
thf(dt_c7_82_1__closure1,axiom,( ( v2_relat_1 @ c7_82_1__closure1 ) & ( m3_pboole @ c7_82_1__closure1 @ ( u1_struct_0 @ c1_82__closure1 ) @ ( k1_mboolean @ ( u1_struct_0 @ c1_82__closure1 ) @ ( u3_msualg_1 @ c1_82__closure1 @ c2_82__closure1 ) ) ) ),file(closure1,c7_82_1__closure1)).
thf(cc3_closure1,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ! [B: $i] : ( ( l1_closure1 @ B @ A ) => ( ( v9_closure1 @ B @ A ) => ( v8_closure1 @ B @ A ) ) ) ) ),file(closure1,cc3_closure1)).
thf(cc4_closure1,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ! [B: $i] : ( ( l1_closure1 @ B @ A ) => ( ( v9_closure1 @ B @ A ) => ( v10_closure1 @ B @ A ) ) ) ) ),file(closure1,cc4_closure1)).
thf(fc7_closure1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( l1_struct_0 @ A ) & ( v9_closure1 @ B @ A ) & ( l1_closure1 @ B @ A ) ) => ( v4_mssubfam @ ( u1_closure1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u3_msualg_1 @ A @ B ) ) ) ),file(closure1,fc7_closure1)).
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(e20_82_1__closure1,conjecture,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ ( u1_struct_0 @ c1_82__closure1 ) ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ ( u1_struct_0 @ c1_82__closure1 ) ) ) => ( ( r1_pboole @ ( u1_struct_0 @ c1_82__closure1 ) @ A @ c7_82_1__closure1 ) <=> ( ( r1_pboole @ ( u1_struct_0 @ c1_82__closure1 ) @ A @ ( u1_closure1 @ c1_82__closure1 @ c2_82__closure1 ) ) & ( r2_pboole @ ( u1_struct_0 @ c1_82__closure1 ) @ c6_82_1__closure1 @ A ) ) ) ) => ( r2_pboole @ ( u1_struct_0 @ c1_82__closure1 ) @ c7_82_1__closure1 @ ( u1_closure1 @ c1_82__closure1 @ c2_82__closure1 ) ) ),file(closure1,e20_82_1__closure1)).
