% Mizar problem: e5_72_1_1,interva1,1610,57 
include('Axioms/SET010^0.ax').
thf(c1_72_type,type,( c1_72__interva1: $i )).
thf(k11_interva1_type,type,( k11_interva1: $i > $i )).
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_binop_1_type,type,( k2_binop_1: $i > $i > $i > $i > $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_interva1_type,type,( k3_interva1: $i > $i > $i > $i )).
thf(k5_binop_1_type,type,( k5_binop_1: $i > $i > $i > $i > $i )).
thf(m1_interva1_type,type,( m1_interva1: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $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_relat_1_type,type,( v1_relat_1: $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(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(dt_k1_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
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(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_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(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_k5_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k5_binop_1 @ A @ B @ C @ D ) @ ( k1_binop_1 @ B @ C @ D ) ) ) ),file(binop_1,k5_binop_1)).
thf(dt_k11_interva1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ~ ( v1_xboole_0 @ ( k11_interva1 @ A ) ) ) ),file(interva1,k11_interva1)).
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_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_interva1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_interva1 @ B @ A ) & ~ ( v1_xboole_0 @ C ) & ( m1_interva1 @ C @ A ) ) => ( m1_interva1 @ ( k3_interva1 @ A @ B @ C ) @ A ) ) ),file(interva1,k3_interva1)).
thf(dt_k5_binop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) & ( m1_subset_1 @ C @ A ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k5_binop_1 @ A @ B @ C @ D ) @ A ) ) ),file(binop_1,k5_binop_1)).
thf(dt_m1_interva1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_interva1 @ B @ A ) => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),file(interva1,m1_interva1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_72__interva1,axiom,( ~ ( v1_xboole_0 @ c1_72__interva1 ) ),file(interva1,c1_72__interva1)).
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_interva1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_interva1 @ B @ A ) & ~ ( v1_xboole_0 @ C ) & ( m1_interva1 @ C @ A ) ) => ~ ( v1_xboole_0 @ ( k3_interva1 @ A @ B @ C ) ) ) ),file(interva1,fc1_interva1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(rc1_interva1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_interva1 @ B @ A ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(interva1,rc1_interva1)).
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(e4_72_1_1__interva1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k11_interva1 @ c1_72__interva1 ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k11_interva1 @ c1_72__interva1 ) ) => ? [C: $i] : ( ( m1_subset_1 @ C @ ( k11_interva1 @ c1_72__interva1 ) ) & ? [D: $i] : ( ~ ( v1_xboole_0 @ D ) & ( m1_interva1 @ D @ c1_72__interva1 ) & ? [E: $i] : ( ~ ( v1_xboole_0 @ E ) & ( m1_interva1 @ E @ c1_72__interva1 ) & ( = @ D @ A ) & ( = @ E @ B ) & ( = @ C @ ( k3_interva1 @ c1_72__interva1 @ D @ E ) ) ) ) ) ) ) ),file(interva1,e4_72_1_1__interva1)).
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(e5_72_1_1__interva1,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ ( k11_interva1 @ c1_72__interva1 ) @ ( k11_interva1 @ c1_72__interva1 ) ) @ ( k11_interva1 @ c1_72__interva1 ) ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k11_interva1 @ c1_72__interva1 ) @ ( k11_interva1 @ c1_72__interva1 ) ) @ ( k11_interva1 @ c1_72__interva1 ) ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( k11_interva1 @ c1_72__interva1 ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k11_interva1 @ c1_72__interva1 ) ) => ? [D: $i] : ( ~ ( v1_xboole_0 @ D ) & ( m1_interva1 @ D @ c1_72__interva1 ) & ? [E: $i] : ( ~ ( v1_xboole_0 @ E ) & ( m1_interva1 @ E @ c1_72__interva1 ) & ( = @ D @ B ) & ( = @ E @ C ) & ( = @ ( k5_binop_1 @ ( k11_interva1 @ c1_72__interva1 ) @ A @ B @ C ) @ ( k3_interva1 @ c1_72__interva1 @ D @ E ) ) ) ) ) ) ) ),file(interva1,e5_72_1_1__interva1)).
