% Mizar problem: e2_136_1_1,valued_2,2458,53 
include('Axioms/SET010^0.ax').
thf(c1_136_type,type,( c1_136__valued_2: $i )).
thf(c2_136_type,type,( c2_136__valued_2: $i )).
thf(c3_136_type,type,( c3_136__valued_2: $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_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k30_valued_1_type,type,( k30_valued_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(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_valued_0_type,type,( v1_valued_0: $i > $o )).
thf(v1_valued_2_type,type,( v1_valued_2: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $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(v7_valued_2_type,type,( v7_valued_2: $i > $o )).
thf(dt_c2_136__valued_2,axiom,( $true ),file(valued_2,c2_136__valued_2)).
thf(cc21_valued_2,axiom,( ! [A: $i] : ( ( v1_valued_2 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v7_valued_2 @ B ) ) ) ) ),file(valued_2,cc21_valued_2)).
thf(cc5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v4_relat_1 @ C @ A ) ) ) ),file(relat_1,cc5_relat_1)).
thf(cc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v5_relat_1 @ C @ A ) ) ) ),file(relat_1,cc6_relat_1)).
thf(cc8_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) ) ) ),file(funct_1,cc8_funct_1)).
thf(cc9_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_funct_1 @ B ) ) ) ),file(funct_1,cc9_funct_1)).
thf(fc111_valued_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_valued_0 @ B ) ) => ( ( v1_relat_1 @ ( k30_valued_1 @ B ) ) & ( v4_relat_1 @ ( k30_valued_1 @ B ) @ A ) & ( v1_funct_1 @ ( k30_valued_1 @ B ) ) & ( v1_valued_0 @ ( k30_valued_1 @ B ) ) ) ) ),file(valued_1,fc111_valued_1)).
thf(fc17_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v4_funct_1 @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ C @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ C @ B ) ) ) ) ),file(funct_1,fc17_funct_1)).
thf(fc40_valued_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v7_valued_2 @ A ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ A @ B ) ) ) ) ),file(valued_2,fc40_valued_2)).
thf(fc42_valued_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v7_valued_2 @ A ) ) => ( v1_valued_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_2,fc42_valued_2)).
thf(rc1_xcmplx_0,axiom,( ? [A: $i] : ( v1_xcmplx_0 @ A ) ),file(xcmplx_0,rc1_xcmplx_0)).
thf(rc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relat_1,rc3_relat_1)).
thf(rc6_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) ) ),file(funct_1,rc6_funct_1)).
thf(involutiveness_k30_valued_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( = @ ( k30_valued_1 @ ( k30_valued_1 @ A ) ) @ A ) ) ),file(valued_1,k30_valued_1)).
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(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_k30_valued_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( ( v1_relat_1 @ ( k30_valued_1 @ A ) ) & ( v1_funct_1 @ ( k30_valued_1 @ A ) ) & ( v1_valued_0 @ ( k30_valued_1 @ A ) ) ) ) ),file(valued_1,k30_valued_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_136__valued_2,axiom,( v1_valued_2 @ c1_136__valued_2 ),file(valued_2,c1_136__valued_2)).
thf(dt_c3_136__valued_2,axiom,( ( v1_funct_1 @ c3_136__valued_2 ) & ( m1_subset_1 @ c3_136__valued_2 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ c1_136__valued_2 @ c2_136__valued_2 ) ) ) ),file(valued_2,c3_136__valued_2)).
thf(cc10_valued_0,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_valued_0 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_valued_0 @ B ) ) ) ),file(valued_0,cc10_valued_0)).
thf(cc15_valued_2,axiom,( ! [A: $i] : ( ( v1_valued_2 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_valued_0 @ B ) ) ) ),file(valued_2,cc15_valued_2)).
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(cc28_valued_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_valued_2 @ B ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_funct_1 @ C ) => ( ( v1_funct_1 @ C ) & ( v7_valued_2 @ C ) ) ) ) ) ),file(valued_2,cc28_valued_2)).
thf(cc2_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_relat_1 @ B ) ) ) ),file(relat_1,cc2_relat_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_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_funct_1 @ B ) ) ) ),file(funct_1,cc3_funct_1)).
thf(cc7_valued_2,axiom,( ! [A: $i] : ( ( v1_valued_2 @ A ) => ( v4_funct_1 @ A ) ) ),file(valued_2,cc7_valued_2)).
thf(cc9_valued_2,axiom,( ! [A: $i] : ( ( v1_valued_2 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_valued_2 @ B ) ) ) ),file(valued_2,cc9_valued_2)).
thf(fc14_valued_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_valued_2 @ C ) & ( v1_funct_1 @ D ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) ) ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ D @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ D @ B ) ) ) ) ),file(valued_2,fc14_valued_2)).
thf(fc16_valued_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_valued_2 @ C ) & ( v1_funct_1 @ D ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) ) ) ) => ( v1_valued_0 @ ( k1_funct_1 @ D @ B ) ) ) ),file(valued_2,fc16_valued_2)).
thf(fc55_valued_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( ( v1_relat_1 @ ( k30_valued_1 @ A ) ) & ( v1_funct_1 @ ( k30_valued_1 @ A ) ) & ( v1_valued_0 @ ( k30_valued_1 @ A ) ) ) ) ),file(valued_1,fc55_valued_1)).
thf(fc61_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( v1_xcmplx_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc61_valued_0)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_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_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e1_136_1_1__valued_2,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ ( k1_relset_1 @ c1_136__valued_2 @ c3_136__valued_2 ) ) & ! [B: $i] : ~ ( ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( v1_valued_0 @ C ) & ( = @ A @ C ) & ( = @ B @ ( k1_funct_1 @ c3_136__valued_2 @ ( k30_valued_1 @ C ) ) ) ) ) ) ),file(valued_2,e1_136_1_1__valued_2)).
thf(s1_classes1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(classes1,s1_classes1)).
thf(e2_136_1_1__valued_2,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k1_relset_1 @ c1_136__valued_2 @ c3_136__valued_2 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k1_relset_1 @ c1_136__valued_2 @ c3_136__valued_2 ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( v1_valued_0 @ C ) & ( = @ B @ C ) & ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ c3_136__valued_2 @ ( k30_valued_1 @ C ) ) ) ) ) ) ),file(valued_2,e2_136_1_1__valued_2)).
