% Mizar problem: e1_94_6_3_1_1_2,lattice3,2295,51 
include('Axioms/SET010^1.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_94_type,type,( c1_94__lattice3: $i )).
thf(c2_94_type,type,( c2_94__lattice3: $i )).
thf(c2_94_6_type,type,( c2_94_6__lattice3: $i )).
thf(c4_94_type,type,( c4_94__lattice3: $i )).
thf(c4_94_6_type,type,( c4_94_6__lattice3: $i )).
thf(g1_orders_2_type,type,( g1_orders_2: $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_tarski_type,type,( k2_tarski: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k9_setfam_1_type,type,( k9_setfam_1: $i > $i )).
thf(u1_orders_2_type,type,( u1_orders_2: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_orders_2_type,type,( l1_orders_2: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_funct_2_type,type,( v1_funct_2: $i > $i > $i > $o )).
thf(v1_orders_2_type,type,( v1_orders_2: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_relat_2_type,type,( v1_relat_2: $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(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_orders_2_type,type,( v2_orders_2: $i > $o )).
thf(v2_relat_2_type,type,( v2_relat_2: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v3_orders_2_type,type,( v3_orders_2: $i > $o )).
thf(v3_relat_2_type,type,( v3_relat_2: $i > $o )).
thf(v4_orders_2_type,type,( v4_orders_2: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_relat_2_type,type,( v4_relat_2: $i > $o )).
thf(v5_orders_2_type,type,( v5_orders_2: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_relat_2_type,type,( v5_relat_2: $i > $o )).
thf(v6_orders_2_type,type,( v6_orders_2: $i > $i > $o )).
thf(v6_relat_2_type,type,( v6_relat_2: $i > $o )).
thf(v7_relat_2_type,type,( v7_relat_2: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_relat_2_type,type,( v8_relat_2: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(cc11_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ) ) ),file(struct_0,cc11_struct_0)).
thf(cc5_subset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,cc5_subset_1)).
thf(rc21_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc21_struct_0)).
thf(rc22_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(struct_0,rc22_struct_0)).
thf(rc2_orders_2,axiom,( ? [A: $i] : ( ( l1_orders_2 @ A ) & ( v13_struct_0 @ A @ np__1 ) & ( v1_orders_2 @ A ) & ( v2_orders_2 @ A ) & ( v3_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( v5_orders_2 @ A ) ) ),file(orders_2,rc2_orders_2)).
thf(rc5_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc5_subset_1)).
thf(rc6_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc6_subset_1)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_u1_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( m1_subset_1 @ ( u1_orders_2 @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ) ) ),file(orders_2,u1_orders_2)).
thf(cc10_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( v13_struct_0 @ A @ np__1 ) ) ) ),file(struct_0,cc10_struct_0)).
thf(cc17_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc17_struct_0)).
thf(cc2_relat_2,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_2 @ A ) & ( v8_relat_2 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) ) ) ),file(relat_2,cc2_relat_2)).
thf(cc2_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc2_struct_0)).
thf(cc3_relat_2,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_relat_2 @ A ) & ( v8_relat_2 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_2 @ A ) ) ) ),file(relat_2,cc3_relat_2)).
thf(cc4_relat_2,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_2 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_2 @ A ) & ( v4_relat_2 @ A ) ) ) ),file(relat_2,cc4_relat_2)).
thf(cc5_relat_2,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v7_relat_2 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) & ( v6_relat_2 @ A ) ) ) ),file(relat_2,cc5_relat_2)).
thf(cc5_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc5_struct_0)).
thf(cc6_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
thf(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc9_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ k1_xboole_0 ) => ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc9_struct_0)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc2_orders_2,axiom,( ! [A: $i] : ( ( ( v2_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ( v1_partfun1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) ) ) ),file(orders_2,fc2_orders_2)).
thf(fc3_orders_2,axiom,( ! [A: $i] : ( ( ( v3_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ( v1_relat_2 @ ( u1_orders_2 @ A ) ) ) ),file(orders_2,fc3_orders_2)).
thf(fc4_orders_2,axiom,( ! [A: $i] : ( ( ( v2_orders_2 @ A ) & ( v5_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ( v4_relat_2 @ ( u1_orders_2 @ A ) ) ) ),file(orders_2,fc4_orders_2)).
thf(fc5_orders_2,axiom,( ! [A: $i] : ( ( ( v2_orders_2 @ A ) & ( v4_orders_2 @ A ) & ( l1_orders_2 @ A ) ) => ( v8_relat_2 @ ( u1_orders_2 @ A ) ) ) ),file(orders_2,fc5_orders_2)).
thf(fc6_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc6_struct_0)).
thf(fc7_struct_0,axiom,( ! [A: $i] : ( ( ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc7_struct_0)).
thf(fc8_struct_0,axiom,( ! [A: $i] : ( ( ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc8_struct_0)).
thf(fc9_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc9_struct_0)).
thf(rc3_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v6_orders_2 @ B @ A ) ) ) ),file(orders_2,rc3_orders_2)).
thf(abstractness_v1_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( v1_orders_2 @ A ) => ( = @ A @ ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ) ),file(orders_2,v1_orders_2)).
thf(dt_l1_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( l1_struct_0 @ A ) ) ),file(orders_2,l1_orders_2)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_c4_94__lattice3,axiom,( ( v1_partfun1 @ c4_94__lattice3 @ c1_94__lattice3 ) & ( v1_relat_2 @ c4_94__lattice3 ) & ( v4_relat_2 @ c4_94__lattice3 ) & ( v8_relat_2 @ c4_94__lattice3 ) & ( m1_subset_1 @ c4_94__lattice3 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ c1_94__lattice3 @ c1_94__lattice3 ) ) ) ),file(lattice3,c4_94__lattice3)).
thf(cc1_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ( ( v3_orders_2 @ A ) => ( v2_orders_2 @ A ) ) ) ),file(orders_2,cc1_orders_2)).
thf(cc1_relat_2,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) & ( v2_relat_2 @ A ) & ( v3_relat_2 @ A ) & ( v4_relat_2 @ A ) & ( v5_relat_2 @ A ) & ( v6_relat_2 @ A ) & ( v7_relat_2 @ A ) & ( v8_relat_2 @ A ) ) ) ),file(relat_2,cc1_relat_2)).
thf(cc1_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc1_struct_0)).
thf(cc2_orders_2,axiom,( ! [A: $i] : ( ( l1_orders_2 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v6_orders_2 @ B @ A ) ) ) ) ),file(orders_2,cc2_orders_2)).
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(cc4_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc4_struct_0)).
thf(cc8_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v13_struct_0 @ A @ k1_xboole_0 ) ) ) ),file(struct_0,cc8_struct_0)).
thf(fc1_struct_0,axiom,( ! [A: $i] : ( ( ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc1_struct_0)).
thf(fc2_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc2_struct_0)).
thf(rc1_orders_2,axiom,( ? [A: $i] : ( ( l1_orders_2 @ A ) & ( v1_orders_2 @ A ) ) ),file(orders_2,rc1_orders_2)).
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_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_orders_2,axiom,( ? [A: $i] : ( ( l1_orders_2 @ A ) & ( v2_struct_0 @ A ) & ( v1_orders_2 @ A ) ) ),file(orders_2,rc4_orders_2)).
thf(rc4_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(struct_0,rc4_struct_0)).
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(free_g1_orders_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ! [C: $i] : ! [D: $i] : ( ( = @ ( g1_orders_2 @ A @ B ) @ ( g1_orders_2 @ C @ D ) ) => ( ( = @ A @ C ) & ( = @ B @ D ) ) ) ) ),file(orders_2,g1_orders_2)).
thf(commutativity_k2_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ B @ A ) ) ),file(tarski,k2_tarski)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k9_setfam_1,axiom,( ! [A: $i] : ( = @ ( k9_setfam_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),file(setfam_1,k9_setfam_1)).
thf(dt_g1_orders_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) ) & ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ) ),file(orders_2,g1_orders_2)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_tarski,axiom,( $true ),file(tarski,k2_tarski)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
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_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_94__lattice3,axiom,( ~ ( v1_xboole_0 @ c1_94__lattice3 ) ),file(lattice3,c1_94__lattice3)).
thf(dt_c2_94__lattice3,axiom,( ( v1_funct_1 @ c2_94__lattice3 ) & ( v1_funct_2 @ c2_94__lattice3 @ ( k9_setfam_1 @ c1_94__lattice3 ) @ c1_94__lattice3 ) & ( m1_subset_1 @ c2_94__lattice3 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k9_setfam_1 @ c1_94__lattice3 ) @ c1_94__lattice3 ) ) ) ),file(lattice3,c2_94__lattice3)).
thf(dt_c2_94_6__lattice3,axiom,( m1_subset_1 @ c2_94_6__lattice3 @ ( k1_zfmisc_1 @ c1_94__lattice3 ) ),file(lattice3,c2_94_6__lattice3)).
thf(dt_c4_94_6__lattice3,axiom,( m1_subset_1 @ c4_94_6__lattice3 @ ( u1_struct_0 @ ( g1_orders_2 @ c1_94__lattice3 @ c4_94__lattice3 ) ) ),file(lattice3,c4_94_6__lattice3)).
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_orders_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) ) => ( ~ ( v2_struct_0 @ ( g1_orders_2 @ A @ B ) ) & ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ) ),file(orders_2,fc1_orders_2)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ) ),file(xboole_0,fc3_xboole_0)).
thf(fc6_orders_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_2 @ B ) & ( v1_partfun1 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) ) => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) ) & ( v3_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ) ),file(orders_2,fc6_orders_2)).
thf(fc7_orders_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v8_relat_2 @ B ) & ( v1_partfun1 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) ) => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) ) & ( v4_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ) ),file(orders_2,fc7_orders_2)).
thf(fc8_orders_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v4_relat_2 @ B ) & ( v1_partfun1 @ B @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) ) => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) ) & ( v5_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ) ),file(orders_2,fc8_orders_2)).
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(e3_94_6_3_1_1__lattice3,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ c1_94__lattice3 ) => ( ( r2_hidden @ A @ c2_94_6__lattice3 ) => ( = @ ( k1_funct_1 @ c2_94__lattice3 @ ( k2_tarski @ A @ c4_94_6__lattice3 ) ) @ c4_94_6__lattice3 ) ) ) ),file(lattice3,e3_94_6_3_1_1__lattice3)).
thf(s6_fraenkel,axiom,( ! [A: $i > $i] : ! [B: $i > $i] : ! [C: $i > $o] : ! [D: $i] : ( ! [E: $i] : ( ( m1_subset_1 @ E @ D ) => ( ( C @ E ) => ( = @ ( B @ E ) @ ( A @ E ) ) ) ) => ( = @ ( replSep1 @ ^ [E: $i] : ( m1_subset_1 @ E @ D ) @ ^ [E: $i] : ( B @ E ) @ ^ [E: $i] : ( C @ E ) ) @ ( replSep1 @ ^ [E: $i] : ( m1_subset_1 @ E @ D ) @ ^ [E: $i] : ( A @ E ) @ ^ [E: $i] : ( C @ E ) ) ) ) ),file(fraenkel,s6_fraenkel)).
thf(e1_94_6_3_1_1_2__lattice3,conjecture,( = @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ c1_94__lattice3 ) @ ^ [A: $i] : ( k1_funct_1 @ c2_94__lattice3 @ ( k2_tarski @ A @ c4_94_6__lattice3 ) ) @ ^ [A: $i] : ( r2_hidden @ A @ c2_94_6__lattice3 ) ) @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ c1_94__lattice3 ) @ ^ [A: $i] : c4_94_6__lattice3 @ ^ [A: $i] : ( r2_hidden @ A @ c2_94_6__lattice3 ) ) ),file(lattice3,e1_94_6_3_1_1_2__lattice3)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
