% Mizar problem: e2_29_5,binop_2,545,17 
include('Axioms/SET010^0.ax').
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_numbers_type,type,( k2_numbers: $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_xcmplx_0_type,type,( k3_xcmplx_0: $i > $i > $i )).
thf(k5_binop_2_type,type,( k5_binop_2: $i > $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(r8_binop_1_type,type,( r8_binop_1: $i > $i > $i > $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_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $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(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(cc1_rat_1,axiom,( ! [A: $i] : ( ( v1_rat_1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(rat_1,cc1_rat_1)).
thf(fc1_rat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_rat_1 @ A ) & ( v1_rat_1 @ B ) ) => ( v1_rat_1 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(rat_1,fc1_rat_1)).
thf(rc2_rat_1,axiom,( ? [A: $i] : ( v1_rat_1 @ A ) ),file(rat_1,rc2_rat_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(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_rat_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v1_rat_1 @ A ) ) ),file(rat_1,cc2_rat_1)).
thf(cc3_int_1,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(int_1,cc3_int_1)).
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(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(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_int_1,axiom,( ? [A: $i] : ( v1_int_1 @ A ) ),file(int_1,rc2_int_1)).
thf(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(cc10_ordinal1,axiom,( ! [A: $i] : ( ( v6_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_ordinal1 @ B ) ) ) ),file(ordinal1,cc10_ordinal1)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc2_int_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_int_1 @ A ) ) ),file(int_1,cc2_int_1)).
thf(cc2_xcmplx_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xcmplx_0,cc2_xcmplx_0)).
thf(cc2_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
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(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc3_ordinal1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) ),file(ordinal1,rc3_ordinal1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
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_k3_xcmplx_0,axiom,( $true ),file(xcmplx_0,k3_xcmplx_0)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
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(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc3_xcmplx_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( v1_xcmplx_0 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(xcmplx_0,fc3_xcmplx_0)).
thf(fc8_xcmplx_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xcmplx_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( v1_xcmplx_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(xcmplx_0,fc8_xcmplx_0)).
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(rc2_xcmplx_0,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_xcmplx_0 @ A ) ) ),file(xcmplx_0,rc2_xcmplx_0)).
thf(commutativity_k5_binop_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k5_binop_2 @ A @ B ) @ ( k5_binop_2 @ B @ A ) ) ) ),file(binop_2,k5_binop_2)).
thf(symmetry_r8_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( 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 ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) => ( ( r8_binop_1 @ A @ B @ C @ D @ E ) => ( r8_binop_1 @ A @ B @ C @ E @ D ) ) ) ),file(binop_1,r8_binop_1)).
thf(reflexivity_r8_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( 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 ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) => ( r8_binop_1 @ A @ B @ C @ D @ D ) ) ),file(binop_1,r8_binop_1)).
thf(redefinition_k5_binop_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( = @ ( k5_binop_2 @ A @ B ) @ ( k3_xcmplx_0 @ A @ B ) ) ) ),file(binop_2,k5_binop_2)).
thf(redefinition_r8_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( 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 ) ) ) & ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) => ( ( r8_binop_1 @ A @ B @ C @ D @ E ) <=> ( = @ D @ E ) ) ) ),file(binop_1,r8_binop_1)).
thf(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_numbers,axiom,( $true ),file(numbers,k2_numbers)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k5_binop_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( m1_subset_1 @ ( k5_binop_2 @ A @ B ) @ k2_numbers ) ) ),file(binop_2,k5_binop_2)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
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(cc3_xcmplx_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k2_numbers ) => ( v1_xcmplx_0 @ A ) ) ),file(xcmplx_0,cc3_xcmplx_0)).
thf(fc2_numbers,axiom,( ~ ( v1_xboole_0 @ k2_numbers ) ),file(numbers,fc2_numbers)).
thf(fc9_numbers,axiom,( ~ ( v1_finset_1 @ k2_numbers ) ),file(numbers,fc9_numbers)).
thf(rc1_xcmplx_0,axiom,( ? [A: $i] : ( v1_xcmplx_0 @ A ) ),file(xcmplx_0,rc1_xcmplx_0)).
thf(s8_binop_2,axiom,( ! [A: $i > $i > $i] : ! [B: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ k2_numbers @ k2_numbers ) @ k2_numbers ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ k2_numbers @ k2_numbers ) @ k2_numbers ) ) ) ) => ! [C: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ k2_numbers @ k2_numbers ) @ k2_numbers ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ k2_numbers @ k2_numbers ) @ k2_numbers ) ) ) ) => ( ( ! [D: $i] : ( ( v1_xcmplx_0 @ D ) => ! [E: $i] : ( ( v1_xcmplx_0 @ E ) => ( = @ ( k1_binop_1 @ B @ D @ E ) @ ( A @ D @ E ) ) ) ) & ! [D: $i] : ( ( v1_xcmplx_0 @ D ) => ! [E: $i] : ( ( v1_xcmplx_0 @ E ) => ( = @ ( k1_binop_1 @ C @ D @ E ) @ ( A @ D @ E ) ) ) ) ) => ( r8_binop_1 @ k2_numbers @ k2_numbers @ k2_numbers @ B @ C ) ) ) ) ),file(binop_2,s8_binop_2)).
thf(e2_29_5__binop_2,conjecture,( ! [A: $i] : ( ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k2_numbers @ k2_numbers ) @ k2_numbers ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ k2_numbers @ k2_numbers ) @ k2_numbers ) ) ) ) => ! [B: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ k2_numbers @ k2_numbers ) @ k2_numbers ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ k2_numbers @ k2_numbers ) @ k2_numbers ) ) ) ) => ( ( ! [C: $i] : ( ( v1_xcmplx_0 @ C ) => ! [D: $i] : ( ( v1_xcmplx_0 @ D ) => ( = @ ( k1_binop_1 @ A @ C @ D ) @ ( k5_binop_2 @ C @ D ) ) ) ) & ! [C: $i] : ( ( v1_xcmplx_0 @ C ) => ! [D: $i] : ( ( v1_xcmplx_0 @ D ) => ( = @ ( k1_binop_1 @ B @ C @ D ) @ ( k5_binop_2 @ C @ D ) ) ) ) ) => ( = @ A @ B ) ) ) ) ),file(binop_2,e2_29_5__binop_2)).
