% Mizar problem: e9_28,topalg_2,770,9 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(g1_pre_topc_type,type,( g1_pre_topc: $i > $i > $i )).
thf(k17_borsuk_1_type,type,( k17_borsuk_1: $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_binop_1_type,type,( k2_binop_1: $i > $i > $i > $i > $i > $i > $i )).
thf(k2_topalg_2_type,type,( k2_topalg_2: $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_topmetr_type,type,( k3_topmetr: $i )).
thf(k3_xcmplx_0_type,type,( k3_xcmplx_0: $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k5_topmetr_type,type,( k5_topmetr: $i )).
thf(u1_pre_topc_type,type,( u1_pre_topc: $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_pre_topc_type,type,( l1_pre_topc: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(m1_pre_topc_type,type,( m1_pre_topc: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_borsuk_2_type,type,( v1_borsuk_2: $i > $o )).
thf(v1_compts_1_type,type,( v1_compts_1: $i > $o )).
thf(v1_connsp_1_type,type,( v1_connsp_1: $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_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_membered_type,type,( v1_membered: $i > $o )).
thf(v1_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_pre_topc_type,type,( v1_pre_topc: $i > $o )).
thf(v1_rat_1_type,type,( v1_rat_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v1_xreal_0_type,type,( v1_xreal_0: $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v1_xxreal_2_type,type,( v1_xxreal_2: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_membered_type,type,( v2_membered: $i > $o )).
thf(v2_pre_topc_type,type,( v2_pre_topc: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_topalg_2_type,type,( v2_topalg_2: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v2_xxreal_2_type,type,( v2_xxreal_2: $i > $o )).
thf(v3_membered_type,type,( v3_membered: $i > $o )).
thf(v3_topmetr_type,type,( v3_topmetr: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v3_xxreal_2_type,type,( v3_xxreal_2: $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v4_pre_topc_type,type,( v4_pre_topc: $i > $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_xxreal_2_type,type,( v4_xxreal_2: $i > $o )).
thf(v5_membered_type,type,( v5_membered: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_xxreal_2_type,type,( v5_xxreal_2: $i > $o )).
thf(v6_membered_type,type,( v6_membered: $i > $o )).
thf(v6_pre_topc_type,type,( v6_pre_topc: $i > $o )).
thf(v6_xxreal_2_type,type,( v6_xxreal_2: $i > $o )).
thf(v7_membered_type,type,( v7_membered: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_pre_topc_type,type,( v7_pre_topc: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_pre_topc_type,type,( v8_pre_topc: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(cc13_xxreal_2,axiom,( ! [A: $i] : ( ( ( v6_membered @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v6_membered @ A ) & ( v1_finset_1 @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc13_xxreal_2)).
thf(cc5_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v3_xxreal_2 @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc5_xxreal_2)).
thf(cc7_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v2_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc7_xxreal_2)).
thf(fc23_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v2_xxreal_0 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc23_xreal_0)).
thf(fc24_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v2_xxreal_0 @ ( k3_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc24_xreal_0)).
thf(fc26_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v3_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v3_xxreal_0 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc26_xreal_0)).
thf(fc59_membered,axiom,( v7_membered @ k4_ordinal1 ),file(membered,fc59_membered)).
thf(fc6_membered,axiom,( v6_membered @ k4_ordinal1 ),file(membered,fc6_membered)).
thf(rc3_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc3_xreal_0)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ A ) ) ) ),file(subset_1,m2_subset_1)).
thf(cc11_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) ) => ( v6_membered @ A ) ) ),file(membered,cc11_membered)).
thf(cc11_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v3_membered @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc11_xxreal_2)).
thf(cc12_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ( v1_finset_1 @ A ) ) ) ),file(xxreal_2,cc12_xxreal_2)).
thf(cc14_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v3_membered @ A ) ) ) ),file(xxreal_2,cc14_xxreal_2)).
thf(cc17_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) ) ),file(xxreal_2,cc17_xxreal_2)).
thf(cc1_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
thf(cc25_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ( v6_membered @ A ) ) ),file(membered,cc25_membered)).
thf(cc4_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v3_xxreal_2 @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc4_xxreal_2)).
thf(cc8_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) => ( v3_membered @ A ) ) ),file(membered,cc8_membered)).
thf(fc11_xxreal_2,axiom,( ~ ( v3_xxreal_2 @ k1_numbers ) & ~ ( v4_xxreal_2 @ k1_numbers ) ),file(xxreal_2,fc11_xxreal_2)).
thf(fc17_xxreal_2,axiom,( v6_xxreal_2 @ k1_numbers ),file(xxreal_2,fc17_xxreal_2)).
thf(fc1_numbers,axiom,( ~ ( v1_xboole_0 @ k1_numbers ) ),file(numbers,fc1_numbers)).
thf(fc25_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v3_xxreal_0 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc25_xreal_0)).
thf(fc3_membered,axiom,( v3_membered @ k1_numbers ),file(membered,fc3_membered)).
thf(fc56_membered,axiom,( v7_membered @ k1_numbers ),file(membered,fc56_membered)).
thf(fc8_numbers,axiom,( ~ ( v1_finset_1 @ k1_numbers ) ),file(numbers,fc8_numbers)).
thf(rc1_rltopsp1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(rltopsp1,rc1_rltopsp1)).
thf(rc1_xxreal_2,axiom,( ? [A: $i] : ( ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v4_membered @ A ) & ( v5_membered @ A ) & ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) ) ),file(xxreal_2,rc1_xxreal_2)).
thf(rc2_xreal_0,axiom,( ? [A: $i] : ( ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc2_xreal_0)).
thf(rc3_topalg_2,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( u1_struct_0 @ k3_topmetr ) ) ) & ~ ( v1_xboole_0 @ A ) & ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v6_xxreal_2 @ A ) ) ),file(topalg_2,rc3_topalg_2)).
thf(rc3_xxreal_2,axiom,( ? [A: $i] : ( ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v4_membered @ A ) & ( v5_membered @ A ) & ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v5_xxreal_2 @ A ) ) ),file(xxreal_2,rc3_xxreal_2)).
thf(rc4_topalg_2,axiom,( ! [A: $i] : ( ( ( v3_topmetr @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v1_membered @ B ) & ( v2_membered @ B ) & ( v3_membered @ B ) & ( v6_xxreal_2 @ B ) ) ) ),file(topalg_2,rc4_topalg_2)).
thf(rc4_xreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) ) ),file(xreal_0,rc4_xreal_0)).
thf(rc4_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc4_xxreal_2)).
thf(rc5_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc5_xxreal_2)).
thf(rc6_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc6_xxreal_2)).
thf(rc7_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) & ~ ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc7_xxreal_2)).
thf(rc8_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ~ ( v1_xxreal_2 @ A ) & ~ ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc8_xxreal_2)).
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(cc12_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xcmplx_0 @ B ) ) ) ),file(membered,cc12_membered)).
thf(cc13_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xxreal_0 @ B ) ) ) ),file(membered,cc13_membered)).
thf(cc15_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_rat_1 @ B ) ) ) ),file(membered,cc15_membered)).
thf(cc15_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v2_membered @ A ) & ( v6_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc15_xxreal_2)).
thf(cc16_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) ) ),file(xxreal_2,cc16_xxreal_2)).
thf(cc19_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_membered @ B ) ) ) ),file(membered,cc19_membered)).
thf(cc20_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_membered @ B ) ) ) ),file(membered,cc20_membered)).
thf(cc22_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_membered @ B ) ) ) ),file(membered,cc22_membered)).
thf(cc2_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc2_xxreal_2)).
thf(cc3_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
thf(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc4_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_0)).
thf(cc6_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v1_finset_1 @ A ) ) => ( ( v3_membered @ A ) & ( v5_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc6_xxreal_2)).
thf(fc6_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc6_xreal_0)).
thf(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc2_xxreal_2,axiom,( ? [A: $i] : ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(xxreal_2,rc2_xxreal_2)).
thf(spc1_numerals,axiom,( ( v2_xxreal_0 @ np__1 ) & ( m2_subset_1 @ np__1 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k5_numbers ) & ( m1_subset_1 @ np__1 @ k1_numbers ) ),file(numerals,spc1_numerals)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(free_g1_pre_topc,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ! [D: $i] : ( ( = @ ( g1_pre_topc @ A @ B ) @ ( g1_pre_topc @ C @ D ) ) => ( ( = @ A @ C ) & ( = @ B @ D ) ) ) ) ),file(pre_topc,g1_pre_topc)).
thf(dt_g1_pre_topc,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ( ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) ) & ( l1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ) ),file(pre_topc,g1_pre_topc)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_u1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),file(pre_topc,u1_pre_topc)).
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(cc10_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v3_membered @ A ) & ( v3_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc10_xxreal_2)).
thf(cc14_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(membered,cc14_membered)).
thf(cc16_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_int_1 @ B ) ) ) ),file(membered,cc16_membered)).
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(cc21_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_membered @ B ) ) ) ),file(membered,cc21_membered)).
thf(cc23_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_membered @ B ) ) ) ),file(membered,cc23_membered)).
thf(cc2_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ( v4_membered @ A ) ) ),file(membered,cc2_membered)).
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(cc2_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
thf(cc4_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
thf(cc5_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v1_membered @ A ) ) ),file(membered,cc5_membered)).
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_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v7_pre_topc @ A ) => ( v6_pre_topc @ A ) ) ) ),file(pre_topc,cc7_pre_topc)).
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(cc8_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v3_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc8_xxreal_2)).
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_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ~ ( v1_xboole_0 @ ( u1_pre_topc @ A ) ) ) ),file(pre_topc,fc1_pre_topc)).
thf(fc6_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ( ( v1_pre_topc @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) & ( v2_pre_topc @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ) ),file(pre_topc,fc6_pre_topc)).
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_pre_topc,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) ) => ( ~ ( v2_struct_0 @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) & ( v1_pre_topc @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ) ),file(pre_topc,fc7_pre_topc)).
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_pre_topc,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) => ( ~ ( v2_struct_0 @ ( g1_pre_topc @ A @ B ) ) & ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ) ),file(pre_topc,fc9_pre_topc)).
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(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(rc6_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ( v4_pre_topc @ B @ A ) ) ) ),file(pre_topc,rc6_pre_topc)).
thf(rc7_pre_topc,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) & ~ ( v1_xboole_0 @ B ) & ( v4_pre_topc @ B @ A ) ) ) ),file(pre_topc,rc7_pre_topc)).
thf(rc9_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v7_pre_topc @ A ) ) ),file(pre_topc,rc9_pre_topc)).
thf(abstractness_v1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v1_pre_topc @ A ) => ( = @ A @ ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ) ),file(pre_topc,v1_pre_topc)).
thf(dt_l1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( l1_struct_0 @ A ) ) ),file(pre_topc,l1_pre_topc)).
thf(cc17_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v7_ordinal1 @ B ) ) ) ),file(membered,cc17_membered)).
thf(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
thf(cc1_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( v2_pre_topc @ B ) ) ) ),file(pre_topc,cc1_pre_topc)).
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(cc1_topmetr,axiom,( ! [A: $i] : ( ( ( v3_topmetr @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( v3_topmetr @ B ) ) ) ),file(topmetr,cc1_topmetr)).
thf(cc24_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_membered @ B ) ) ) ),file(membered,cc24_membered)).
thf(cc2_borsuk_2,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_borsuk_2 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v2_pre_topc @ A ) & ( v1_connsp_1 @ A ) ) ) ) ),file(borsuk_2,cc2_borsuk_2)).
thf(cc2_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) => ( ( v1_xboole_0 @ B ) => ( v4_pre_topc @ B @ A ) ) ) ) ),file(pre_topc,cc2_pre_topc)).
thf(cc2_zfmisc_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(zfmisc_1,cc2_zfmisc_1)).
thf(cc3_topalg_2,axiom,( ! [A: $i] : ( ( m1_pre_topc @ A @ k2_topalg_2 ) => ( ( ~ ( v2_struct_0 @ A ) & ( v2_topalg_2 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_borsuk_2 @ A ) ) ) ) ),file(topalg_2,cc3_topalg_2)).
thf(cc3_xxreal_2,axiom,( ! [A: $i] : ( ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) => ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc3_xxreal_2)).
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_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v8_pre_topc @ A ) => ( v7_pre_topc @ A ) ) ) ),file(pre_topc,cc8_pre_topc)).
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(cc9_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ( ( v2_struct_0 @ A ) => ( v6_pre_topc @ A ) ) ) ),file(pre_topc,cc9_pre_topc)).
thf(cc9_xxreal_2,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( ( v6_membered @ A ) & ( v3_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc9_xxreal_2)).
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(fc4_topmetr,axiom,( ! [A: $i] : ( ( ( v3_topmetr @ A ) & ( l1_struct_0 @ A ) ) => ( v3_membered @ ( u1_struct_0 @ A ) ) ) ),file(topmetr,fc4_topmetr)).
thf(rc11_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ( v2_struct_0 @ A ) & ( v1_pre_topc @ A ) ) ),file(pre_topc,rc11_pre_topc)).
thf(rc12_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ( v2_struct_0 @ A ) & ( v1_pre_topc @ A ) & ( v2_pre_topc @ A ) ) ),file(pre_topc,rc12_pre_topc)).
thf(rc1_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc1_membered)).
thf(rc1_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ( v1_pre_topc @ A ) ) ),file(pre_topc,rc1_pre_topc)).
thf(rc1_zfmisc_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) ),file(zfmisc_1,rc1_zfmisc_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(rc2_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc2_membered)).
thf(rc2_pre_topc,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ~ ( v2_struct_0 @ A ) & ( v1_pre_topc @ A ) & ( v2_pre_topc @ A ) ) ),file(pre_topc,rc2_pre_topc)).
thf(rc2_zfmisc_1,axiom,( ? [A: $i] : ~ ( v1_zfmisc_1 @ A ) ),file(zfmisc_1,rc2_zfmisc_1)).
thf(rc3_borsuk_2,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ~ ( v2_struct_0 @ A ) & ( v1_pre_topc @ A ) & ( v2_pre_topc @ A ) & ( v1_borsuk_2 @ A ) ) ),file(borsuk_2,rc3_borsuk_2)).
thf(rc3_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) & ( v7_membered @ A ) ) ),file(membered,rc3_membered)).
thf(rc3_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ? [B: $i] : ( ( m1_pre_topc @ B @ A ) & ( v1_pre_topc @ B ) ) ) ),file(pre_topc,rc3_pre_topc)).
thf(rc3_topmetr,axiom,( ? [A: $i] : ( ( l1_struct_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v3_topmetr @ A ) ) ),file(topmetr,rc3_topmetr)).
thf(rc4_pre_topc,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_pre_topc @ B @ A ) & ~ ( v2_struct_0 @ B ) & ( v1_pre_topc @ B ) ) ) ),file(pre_topc,rc4_pre_topc)).
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_topmetr,axiom,( ? [A: $i] : ( ( l1_pre_topc @ A ) & ~ ( v2_struct_0 @ A ) & ( v1_pre_topc @ A ) & ( v2_pre_topc @ A ) & ( v3_topmetr @ A ) ) ),file(topmetr,rc4_topmetr)).
thf(rc5_pre_topc,axiom,( ! [A: $i] : ( ( ( v2_pre_topc @ A ) & ( l1_pre_topc @ A ) ) => ? [B: $i] : ( ( m1_pre_topc @ B @ A ) & ( v1_pre_topc @ B ) & ( v2_pre_topc @ B ) ) ) ),file(pre_topc,rc5_pre_topc)).
thf(rc5_topalg_2,axiom,( ? [A: $i] : ( ( m1_pre_topc @ A @ k3_topmetr ) & ~ ( v2_struct_0 @ A ) & ( v1_pre_topc @ A ) & ( v2_pre_topc @ A ) & ( v3_topmetr @ A ) & ( v2_topalg_2 @ A ) ) ),file(topalg_2,rc5_topalg_2)).
thf(dt_k17_borsuk_1,axiom,( l1_pre_topc @ k17_borsuk_1 ),file(borsuk_1,k17_borsuk_1)).
thf(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k3_topmetr,axiom,( ( v2_pre_topc @ k3_topmetr ) & ( l1_pre_topc @ k3_topmetr ) ),file(topmetr,k3_topmetr)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_m1_pre_topc,axiom,( ! [A: $i] : ( ( l1_pre_topc @ A ) => ! [B: $i] : ( ( m1_pre_topc @ B @ A ) => ( l1_pre_topc @ B ) ) ) ),file(pre_topc,m1_pre_topc)).
thf(cc18_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_membered)).
thf(cc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_partfun1 @ C @ A ) => ( v1_funct_2 @ C @ A @ B ) ) ) ),file(funct_2,cc1_funct_2)).
thf(cc1_zfmisc_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_zfmisc_1 @ A ) ) ),file(zfmisc_1,cc1_zfmisc_1)).
thf(cc26_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_membered @ A ) ) ),file(membered,cc26_membered)).
thf(cc2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc2_funct_2)).
thf(cc3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_2 @ C @ A @ B ) => ( v1_partfun1 @ C @ A ) ) ) ) ),file(funct_2,cc3_funct_2)).
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(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(cc8_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ~ ( v1_xboole_0 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ),file(funct_2,cc8_funct_2)).
thf(fc2_topmetr,axiom,( ~ ( v2_struct_0 @ k3_topmetr ) & ( v1_pre_topc @ k3_topmetr ) & ( v2_pre_topc @ k3_topmetr ) ),file(topmetr,fc2_topmetr)).
thf(fc3_topmetr,axiom,( v3_topmetr @ k17_borsuk_1 ),file(topmetr,fc3_topmetr)).
thf(fc3_zfmisc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ B ) => ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(zfmisc_1,fc3_zfmisc_1)).
thf(fc4_zfmisc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(zfmisc_1,fc4_zfmisc_1)).
thf(fc5_topmetr,axiom,( ( v2_pre_topc @ k3_topmetr ) & ( v3_topmetr @ k3_topmetr ) ),file(topmetr,fc5_topmetr)).
thf(fc8_borsuk_2,axiom,( ( v8_pre_topc @ k17_borsuk_1 ) & ( v1_compts_1 @ k17_borsuk_1 ) ),file(borsuk_2,fc8_borsuk_2)).
thf(fc9_borsuk_1,axiom,( ~ ( v2_struct_0 @ k17_borsuk_1 ) & ( v1_pre_topc @ k17_borsuk_1 ) & ( v2_pre_topc @ k17_borsuk_1 ) ),file(borsuk_1,fc9_borsuk_1)).
thf(fc9_borsuk_2,axiom,( v1_borsuk_2 @ k17_borsuk_1 ),file(borsuk_2,fc9_borsuk_2)).
thf(rc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) ),file(funct_2,rc1_funct_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(commutativity_k3_xcmplx_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k3_xcmplx_0 @ A @ B ) @ ( k3_xcmplx_0 @ B @ A ) ) ) ),file(xcmplx_0,k3_xcmplx_0)).
thf(redefinition_k2_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) ) => ( = @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_binop_1 @ D @ E @ F ) ) ) ),file(binop_1,k2_binop_1)).
thf(redefinition_k2_topalg_2,axiom,( = @ k2_topalg_2 @ k3_topmetr ),file(topalg_2,k2_topalg_2)).
thf(redefinition_k5_topmetr,axiom,( = @ k5_topmetr @ k17_borsuk_1 ),file(topmetr,k5_topmetr)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) ) => ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ) ),file(binop_1,k2_binop_1)).
thf(dt_k2_topalg_2,axiom,( ( v2_topalg_2 @ k2_topalg_2 ) & ( m1_pre_topc @ k2_topalg_2 @ k3_topmetr ) ),file(topalg_2,k2_topalg_2)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_xcmplx_0,axiom,( $true ),file(xcmplx_0,k3_xcmplx_0)).
thf(dt_k5_topmetr,axiom,( m1_pre_topc @ k5_topmetr @ k3_topmetr ),file(topmetr,k5_topmetr)).
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(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(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(cc4_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_funct_2 @ B @ A @ A ) => ( v1_partfun1 @ B @ A ) ) ) ),file(funct_2,cc4_funct_2)).
thf(e8_28__topalg_2,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( u1_struct_0 @ k2_topalg_2 ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ k5_topmetr ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ k2_topalg_2 ) ) & ( = @ C @ ( k3_xcmplx_0 @ B @ A ) ) ) ) ) ),file(topalg_2,e8_28__topalg_2)).
thf(s3_binop_1,axiom,( ! [A: $i > $i > $i > $o] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ! [E: $i] : ( ( m1_subset_1 @ E @ D ) => ! [F: $i] : ( ( m1_subset_1 @ F @ C ) => ? [G: $i] : ( ( m1_subset_1 @ G @ B ) & ( A @ E @ F @ G ) ) ) ) => ? [E: $i] : ( ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ C ) @ B ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ D @ C ) @ B ) ) ) & ! [F: $i] : ( ( m1_subset_1 @ F @ D ) => ! [G: $i] : ( ( m1_subset_1 @ G @ C ) => ( A @ F @ G @ ( k2_binop_1 @ D @ C @ B @ E @ F @ G ) ) ) ) ) ) ),file(binop_1,s3_binop_1)).
thf(e9_28__topalg_2,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ ( u1_struct_0 @ k2_topalg_2 ) @ ( u1_struct_0 @ k5_topmetr ) ) @ ( u1_struct_0 @ k2_topalg_2 ) ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( u1_struct_0 @ k2_topalg_2 ) @ ( u1_struct_0 @ k5_topmetr ) ) @ ( u1_struct_0 @ k2_topalg_2 ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ k2_topalg_2 ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( u1_struct_0 @ k5_topmetr ) ) => ( = @ ( k2_binop_1 @ ( u1_struct_0 @ k2_topalg_2 ) @ ( u1_struct_0 @ k5_topmetr ) @ ( u1_struct_0 @ k2_topalg_2 ) @ A @ B @ C ) @ ( k3_xcmplx_0 @ C @ B ) ) ) ) ) ),file(topalg_2,e9_28__topalg_2)).
