% Mizar problem: e6_94_2,lattice3,2205,47 
include('Axioms/SET010^1.ax').
thf(c1_94_type,type,( c1_94__lattice3: $i )).
thf(c1_94_2_type,type,( c1_94_2__lattice3: $i )).
thf(c2_94_type,type,( c2_94__lattice3: $i )).
thf(c3_94_2_type,type,( c3_94_2__lattice3: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_relset_1_type,type,( k1_relset_1: $i > $i > $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(k3_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k7_domain_1_type,type,( k7_domain_1: $i > $i > $i > $i )).
thf(k7_relat_1_type,type,( k7_relat_1: $i > $i > $i )).
thf(k7_relset_1_type,type,( k7_relset_1: $i > $i > $i > $i > $i )).
thf(k9_setfam_1_type,type,( k9_setfam_1: $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $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_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(v2_relat_2_type,type,( v2_relat_2: $i > $o )).
thf(v3_relat_2_type,type,( v3_relat_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_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_relat_2_type,type,( v5_relat_2: $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(v8_relat_2_type,type,( v8_relat_2: $i > $o )).
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(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(commutativity_k2_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ B @ A ) ) ),file(tarski,k2_tarski)).
thf(dt_k2_tarski,axiom,( $true ),file(tarski,k2_tarski)).
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(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(fc11_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ) => ~ ( v1_xboole_0 @ ( k7_relat_1 @ A @ B ) ) ) ),file(relset_1,fc11_relset_1)).
thf(fc3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ) ),file(xboole_0,fc3_xboole_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(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(commutativity_k7_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) & ( m1_subset_1 @ C @ A ) ) => ( = @ ( k7_domain_1 @ A @ B @ C ) @ ( k7_domain_1 @ A @ C @ B ) ) ) ),file(domain_1,k7_domain_1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( = @ ( k1_relset_1 @ A @ B ) @ ( k9_xtuple_0 @ B ) ) ) ),file(relset_1,k1_relset_1)).
thf(redefinition_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(funct_2,k3_funct_2)).
thf(redefinition_k7_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) & ( m1_subset_1 @ C @ A ) ) => ( = @ ( k7_domain_1 @ A @ B @ C ) @ ( k2_tarski @ B @ C ) ) ) ),file(domain_1,k7_domain_1)).
thf(redefinition_k7_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( = @ ( k7_relset_1 @ A @ B @ C @ D ) @ ( k7_relat_1 @ C @ D ) ) ) ),file(relset_1,k7_relset_1)).
thf(redefinition_k9_setfam_1,axiom,( ! [A: $i] : ( = @ ( k9_setfam_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),file(setfam_1,k9_setfam_1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( m1_subset_1 @ ( k1_relset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(relset_1,k1_relset_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ B ) ) ),file(funct_2,k3_funct_2)).
thf(dt_k7_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( m1_subset_1 @ B @ A ) & ( m1_subset_1 @ C @ A ) ) => ( m1_subset_1 @ ( k7_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(domain_1,k7_domain_1)).
thf(dt_k7_relat_1,axiom,( $true ),file(relat_1,k7_relat_1)).
thf(dt_k7_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( m1_subset_1 @ ( k7_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ) ),file(relset_1,k7_relset_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_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_94__lattice3,axiom,( ~ ( v1_xboole_0 @ c1_94__lattice3 ) ),file(lattice3,c1_94__lattice3)).
thf(dt_c1_94_2__lattice3,axiom,( m1_subset_1 @ c1_94_2__lattice3 @ c1_94__lattice3 ),file(lattice3,c1_94_2__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_c3_94_2__lattice3,axiom,( m1_subset_1 @ c3_94_2__lattice3 @ ( k1_zfmisc_1 @ c1_94__lattice3 ) ),file(lattice3,c3_94_2__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_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc8_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) => ( v1_relat_1 @ ( k9_xtuple_0 @ D ) ) ) ),file(relset_1,fc8_relset_1)).
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(e5_94_2__lattice3,axiom,( r1_tarski @ ( k9_setfam_1 @ c1_94__lattice3 ) @ ( k1_relset_1 @ ( k9_setfam_1 @ c1_94__lattice3 ) @ c2_94__lattice3 ) ),file(lattice3,e5_94_2__lattice3)).
thf(s2_lattice3,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i > $i] : ! [D: $i] : ! [E: $i] : ( ( ~ ( v1_xboole_0 @ E ) & ~ ( v1_xboole_0 @ D ) & ! [F: $i] : ( m1_subset_1 @ ( C @ F ) @ D ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( r1_tarski @ D @ ( k9_xtuple_0 @ B ) ) => ( = @ ( k7_relat_1 @ B @ ( replSep1 @ ^ [G: $i] : ( m1_subset_1 @ G @ E ) @ ^ [G: $i] : ( C @ G ) @ ^ [G: $i] : ( A @ G ) ) ) @ ( replSep1 @ ^ [G: $i] : ( m1_subset_1 @ G @ E ) @ ^ [G: $i] : ( k1_funct_1 @ B @ ( C @ G ) ) @ ^ [G: $i] : ( A @ G ) ) ) ) ) ),file(lattice3,s2_lattice3)).
thf(e6_94_2__lattice3,conjecture,( = @ ( k7_relset_1 @ ( k9_setfam_1 @ c1_94__lattice3 ) @ c1_94__lattice3 @ c2_94__lattice3 @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ c1_94__lattice3 ) @ ^ [A: $i] : ( k7_domain_1 @ c1_94__lattice3 @ A @ c1_94_2__lattice3 ) @ ^ [A: $i] : ( r2_hidden @ A @ c3_94_2__lattice3 ) ) ) @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ c1_94__lattice3 ) @ ^ [A: $i] : ( k3_funct_2 @ ( k1_zfmisc_1 @ c1_94__lattice3 ) @ c1_94__lattice3 @ c2_94__lattice3 @ ( k7_domain_1 @ c1_94__lattice3 @ A @ c1_94_2__lattice3 ) ) @ ^ [A: $i] : ( r2_hidden @ A @ c3_94_2__lattice3 ) ) ),file(lattice3,e6_94_2__lattice3)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
