% Mizar problem: s1_fib_num,fib_num,191,8 
include('Axioms/SET010^0.ax').
thf(n0_type,type,( np__0: $i )).
thf(n1_type,type,( np__1: $i )).
thf(n2_type,type,( np__2: $i )).
thf(k1_nat_1_type,type,( k1_nat_1: $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_nat_1_type,type,( k2_nat_1: $i > $i > $i )).
thf(k2_xcmplx_0_type,type,( k2_xcmplx_0: $i > $i > $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(k6_numbers_type,type,( k6_numbers: $i )).
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(p1_s1_fib_num_type,type,( p1_s1_fib_num: $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_membered_type,type,( v1_membered: $i > $o )).
thf(v1_rat_1_type,type,( v1_rat_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_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_membered_type,type,( v2_membered: $i > $o )).
thf(v2_setfam_1_type,type,( v2_setfam_1: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_membered_type,type,( v3_membered: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_membered_type,type,( v5_membered: $i > $o )).
thf(v6_membered_type,type,( v6_membered: $i > $o )).
thf(v7_membered_type,type,( v7_membered: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(cc11_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) ) => ( v6_membered @ A ) ) ),file(membered,cc11_membered)).
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(cc14_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(membered,cc14_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(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_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v7_ordinal1 @ B ) ) ) ),file(membered,cc17_membered)).
thf(cc18_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_membered)).
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(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
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(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(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(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(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(cc25_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ( v6_membered @ A ) ) ),file(membered,cc25_membered)).
thf(cc26_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_membered @ A ) ) ),file(membered,cc26_membered)).
thf(cc2_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc2_finset_1)).
thf(cc2_int_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_int_1 @ A ) ) ),file(int_1,cc2_int_1)).
thf(cc2_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ( v4_membered @ A ) ) ),file(membered,cc2_membered)).
thf(cc2_nat_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ~ ( v3_xxreal_0 @ A ) ) ),file(nat_1,cc2_nat_1)).
thf(cc2_setfam_1,axiom,( ! [A: $i] : ( ~ ( v2_setfam_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(setfam_1,cc2_setfam_1)).
thf(cc2_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
thf(cc3_int_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(int_1,cc3_int_1)).
thf(cc3_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc4_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
thf(cc4_setfam_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ~ ( v2_setfam_1 @ A ) ) ),file(setfam_1,cc4_setfam_1)).
thf(cc4_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_0)).
thf(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(cc5_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v1_membered @ A ) ) ),file(membered,cc5_membered)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
thf(cc7_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc7_finset_1)).
thf(cc8_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_finset_1 @ B ) ) ) ),file(finset_1,cc8_finset_1)).
thf(cc8_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) => ( v3_membered @ A ) ) ),file(membered,cc8_membered)).
thf(commutativity_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( = @ ( k1_nat_1 @ A @ B ) @ ( k1_nat_1 @ B @ A ) ) ) ),file(nat_1,k1_nat_1)).
thf(commutativity_k2_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k2_nat_1 @ A @ B ) @ ( k2_nat_1 @ B @ A ) ) ) ),file(nat_1,k2_nat_1)).
thf(commutativity_k2_xcmplx_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k2_xcmplx_0 @ A @ B ) @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xcmplx_0,k2_xcmplx_0)).
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(dt_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( m2_subset_1 @ ( k1_nat_1 @ A @ B ) @ k1_numbers @ k5_numbers ) ) ),file(nat_1,k1_nat_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( v7_ordinal1 @ B ) ) => ( m2_subset_1 @ ( k2_nat_1 @ A @ B ) @ k1_numbers @ k5_numbers ) ) ),file(nat_1,k2_nat_1)).
thf(dt_k2_xcmplx_0,axiom,( $true ),file(xcmplx_0,k2_xcmplx_0)).
thf(dt_k3_xcmplx_0,axiom,( $true ),file(xcmplx_0,k3_xcmplx_0)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k6_numbers,axiom,( m2_subset_1 @ k6_numbers @ k1_numbers @ k5_numbers ),file(numbers,k6_numbers)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
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(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(existence_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 ) ) ),file(subset_1,m2_subset_1)).
thf(fc10_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v2_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ~ ( v2_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc10_xreal_0)).
thf(fc11_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 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc11_xreal_0)).
thf(fc12_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 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc12_xreal_0)).
thf(fc13_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc13_xreal_0)).
thf(fc14_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_xxreal_0 @ A ) & ( v1_xreal_0 @ A ) & ~ ( v2_xxreal_0 @ B ) & ( v1_xreal_0 @ B ) ) => ( v3_xxreal_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(xreal_0,fc14_xreal_0)).
thf(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_1)).
thf(fc1_int_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( v1_int_1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(int_1,fc1_int_1)).
thf(fc1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( v7_ordinal1 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,fc1_nat_1)).
thf(fc1_numbers,axiom,( ~ ( v1_xboole_0 @ k1_numbers ) ),file(numbers,fc1_numbers)).
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(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(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(fc2_int_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( v1_int_1 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(int_1,fc2_int_1)).
thf(fc2_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( v7_ordinal1 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,fc2_nat_1)).
thf(fc31_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc31_finset_1)).
thf(fc3_membered,axiom,( v3_membered @ k1_numbers ),file(membered,fc3_membered)).
thf(fc3_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v7_ordinal1 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,fc3_nat_1)).
thf(fc4_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v7_ordinal1 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_xcmplx_0 @ B @ A ) ) ) ),file(nat_1,fc4_nat_1)).
thf(fc56_membered,axiom,( v7_membered @ k1_numbers ),file(membered,fc56_membered)).
thf(fc59_membered,axiom,( v7_membered @ k4_ordinal1 ),file(membered,fc59_membered)).
thf(fc5_xreal_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v1_xreal_0 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc5_xreal_0)).
thf(fc6_membered,axiom,( v6_membered @ k4_ordinal1 ),file(membered,fc6_membered)).
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(fc8_numbers,axiom,( ~ ( v1_finset_1 @ k1_numbers ) ),file(numbers,fc8_numbers)).
thf(fc9_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 @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(xreal_0,fc9_xreal_0)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_int_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) & ( v1_xxreal_0 @ A ) & ( v1_xcmplx_0 @ A ) & ( v1_xreal_0 @ A ) & ( v1_int_1 @ A ) ) ),file(int_1,rc1_int_1)).
thf(rc1_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc1_membered)).
thf(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc2_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc2_finset_1)).
thf(rc2_int_1,axiom,( ? [A: $i] : ( v1_int_1 @ A ) ),file(int_1,rc2_int_1)).
thf(rc2_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc2_membered)).
thf(rc2_nat_1,axiom,( ? [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) & ~ ( v1_xboole_0 @ A ) & ( v3_ordinal1 @ A ) ) ),file(nat_1,rc2_nat_1)).
thf(rc2_setfam_1,axiom,( ? [A: $i] : ~ ( v2_setfam_1 @ A ) ),file(setfam_1,rc2_setfam_1)).
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_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) & ( v7_membered @ A ) ) ),file(membered,rc3_membered)).
thf(rc3_setfam_1,axiom,( ! [A: $i] : ( ~ ( v2_setfam_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(setfam_1,rc3_setfam_1)).
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(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(rc7_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc7_finset_1)).
thf(rc8_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(redefinition_k1_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( = @ ( k1_nat_1 @ A @ B ) @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,k1_nat_1)).
thf(redefinition_k2_nat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( v7_ordinal1 @ B ) ) => ( = @ ( k2_nat_1 @ A @ B ) @ ( k2_xcmplx_0 @ A @ B ) ) ) ),file(nat_1,k2_nat_1)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_k6_numbers,axiom,( = @ k6_numbers @ k1_xboole_0 ),file(numbers,k6_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(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(rqRealAdd__k2_xcmplx_0__r0_r0_r0,axiom,( = @ ( k2_xcmplx_0 @ np__0 @ np__0 ) @ np__0 ),file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)).
thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1,axiom,( = @ ( k2_xcmplx_0 @ np__0 @ np__1 ) @ np__1 ),file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r0_r2_r2,axiom,( = @ ( k2_xcmplx_0 @ np__0 @ np__2 ) @ np__2 ),file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2)).
thf(rqRealAdd__k2_xcmplx_0__r1_r0_r1,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ np__0 ) @ np__1 ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)).
thf(rqRealAdd__k2_xcmplx_0__r1_r1_r2,axiom,( = @ ( k2_xcmplx_0 @ np__1 @ np__1 ) @ np__2 ),file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)).
thf(rqRealAdd__k2_xcmplx_0__r2_r0_r2,axiom,( = @ ( k2_xcmplx_0 @ np__2 @ np__0 ) @ np__2 ),file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2)).
thf(rqRealMult__k3_xcmplx_0__r0_r0_r0,axiom,( = @ ( k3_xcmplx_0 @ np__0 @ np__0 ) @ np__0 ),file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r1_r0,axiom,( = @ ( k3_xcmplx_0 @ np__0 @ np__1 ) @ np__0 ),file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r2_r0,axiom,( = @ ( k3_xcmplx_0 @ np__0 @ np__2 ) @ np__0 ),file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0)).
thf(rqRealMult__k3_xcmplx_0__r1_r0_r0,axiom,( = @ ( k3_xcmplx_0 @ np__1 @ np__0 ) @ np__0 ),file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r1_r1_r1,axiom,( = @ ( k3_xcmplx_0 @ np__1 @ np__1 ) @ np__1 ),file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)).
thf(rqRealMult__k3_xcmplx_0__r1_r2_r2,axiom,( = @ ( k3_xcmplx_0 @ np__1 @ np__2 ) @ np__2 ),file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2)).
thf(rqRealMult__k3_xcmplx_0__r2_r0_r0,axiom,( = @ ( k3_xcmplx_0 @ np__2 @ np__0 ) @ np__0 ),file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r2_r1_r2,axiom,( = @ ( k3_xcmplx_0 @ np__2 @ np__1 ) @ np__2 ),file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2)).
thf(spc0_boole,axiom,( v1_xboole_0 @ np__0 ),file(boole,spc0_boole)).
thf(spc0_numerals,axiom,( ( m2_subset_1 @ np__0 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__0 @ k5_numbers ) & ( m1_subset_1 @ np__0 @ k1_numbers ) ),file(numerals,spc0_numerals)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
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(spc2_boole,axiom,( ~ ( v1_xboole_0 @ np__2 ) ),file(boole,spc2_boole)).
thf(spc2_numerals,axiom,( ( v2_xxreal_0 @ np__2 ) & ( m2_subset_1 @ np__2 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__2 @ k5_numbers ) & ( m1_subset_1 @ np__2 @ k1_numbers ) ),file(numerals,spc2_numerals)).
thf(spc5_arithm,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) & ( v1_xcmplx_0 @ C ) ) => ( = @ ( k3_xcmplx_0 @ ( k2_xcmplx_0 @ A @ B ) @ C ) @ ( k2_xcmplx_0 @ ( k3_xcmplx_0 @ A @ C ) @ ( k3_xcmplx_0 @ B @ C ) ) ) ) ),file(arithm,spc5_arithm)).
thf(spc6_arithm,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) & ( v1_xcmplx_0 @ C ) ) => ( = @ ( k2_xcmplx_0 @ ( k2_xcmplx_0 @ A @ B ) @ C ) @ ( k2_xcmplx_0 @ A @ ( k2_xcmplx_0 @ B @ C ) ) ) ) ),file(arithm,spc6_arithm)).
thf(spc7_arithm,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) & ( v1_xcmplx_0 @ C ) ) => ( = @ ( k3_xcmplx_0 @ ( k3_xcmplx_0 @ A @ B ) @ C ) @ ( k3_xcmplx_0 @ A @ ( k3_xcmplx_0 @ B @ C ) ) ) ) ),file(arithm,spc6_arithm)).
thf(t1_arithm,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( = @ ( k2_xcmplx_0 @ A @ k6_numbers ) @ A ) ) ),file(arithm,t1_arithm)).
thf(t1_numerals,axiom,( m1_subset_1 @ k1_xboole_0 @ k4_ordinal1 ),file(numerals,t1_numerals)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t2_arithm,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( = @ ( k3_xcmplx_0 @ A @ k6_numbers ) @ k6_numbers ) ) ),file(arithm,t2_arithm)).
thf(t2_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ B ) => ( ( v1_xboole_0 @ B ) | ( r2_hidden @ A @ B ) ) ) ),file(subset,t2_subset)).
thf(t3_arithm,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( = @ ( k3_xcmplx_0 @ np__1 @ A ) @ A ) ) ),file(arithm,t3_arithm)).
thf(t3_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) <=> ( r1_tarski @ A @ B ) ) ),file(subset,t3_subset)).
thf(t4_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) ) => ( m1_subset_1 @ A @ C ) ) ),file(subset,t4_subset)).
thf(t5_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ~ ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) & ( v1_xboole_0 @ C ) ) ),file(subset,t5_subset)).
thf(t6_boole,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( = @ A @ k1_xboole_0 ) ) ),file(boole,t6_boole)).
thf(t7_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t7_boole)).
thf(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
thf(s2_nat_1,axiom,( ! [A: $i > $o] : ( ( ( A @ k6_numbers ) & ! [B: $i] : ( ( v7_ordinal1 @ B ) => ( ( A @ B ) => ( A @ ( k1_nat_1 @ B @ np__1 ) ) ) ) ) => ! [B: $i] : ( ( v7_ordinal1 @ B ) => ( A @ B ) ) ) ),file(nat_1,s2_nat_1)).
thf(s1_fib_num,conjecture,( ( ( p1_s1_fib_num @ k6_numbers ) & ( p1_s1_fib_num @ np__1 ) & ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( ( p1_s1_fib_num @ A ) & ( p1_s1_fib_num @ ( k1_nat_1 @ A @ np__1 ) ) ) => ( p1_s1_fib_num @ ( k1_nat_1 @ A @ np__2 ) ) ) ) ) => ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( p1_s1_fib_num @ A ) ) ),file(fib_num,s1_fib_num)).
