% Mizar problem: e4_30_1,zf_refle,689,56 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_30_type,type,( c1_30__zf_refle: $i )).
thf(c1_30_1_type,type,( c1_30_1__zf_refle: $i )).
thf(c2_30_type,type,( c2_30__zf_refle: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_funct_2_type,type,( k1_funct_2: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zf_lang_type,type,( k1_zf_lang: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k23_zf_lang_type,type,( k23_zf_lang: $i > $i )).
thf(k24_zf_lang_type,type,( k24_zf_lang: $i > $i )).
thf(k2_funct_7_type,type,( k2_funct_7: $i > $i > $i > $i )).
thf(k2_ordinal4_type,type,( k2_ordinal4: $i > $i )).
thf(k2_zf_lang1_type,type,( k2_zf_lang1: $i > $i > $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_card_3_type,type,( k3_card_3: $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_zf_refle_type,type,( k4_zf_refle: $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_zf_lang_type,type,( k6_zf_lang: $i > $i )).
thf(k9_funct_2_type,type,( k9_funct_2: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(m1_finseq_1_type,type,( m1_finseq_1: $i > $i > $o )).
thf(m1_funct_2_type,type,( m1_funct_2: $i > $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_finseq_1_type,type,( m2_finseq_1: $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r1_zf_model_type,type,( r1_zf_model: $i > $i > $i > $o )).
thf(v1_card_1_type,type,( v1_card_1: $i > $o )).
thf(v1_card_3_type,type,( v1_card_3: $i > $o )).
thf(v1_card_5_type,type,( v1_card_5: $i > $o )).
thf(v1_classes1_type,type,( v1_classes1: $i > $o )).
thf(v1_classes2_type,type,( v1_classes2: $i > $o )).
thf(v1_finseq_1_type,type,( v1_finseq_1: $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_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_ordinal2_type,type,( v1_ordinal2: $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(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_zf_lang_type,type,( v1_zf_lang: $i > $o )).
thf(v1_zf_refle_type,type,( v1_zf_refle: $i > $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_card_1_type,type,( v2_card_1: $i > $o )).
thf(v2_classes1_type,type,( v2_classes1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_card_1_type,type,( v3_card_1: $i > $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v4_card_3_type,type,( v4_card_3: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_ordinal1_type,type,( v4_ordinal1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_card_3_type,type,( v5_card_3: $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(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(cc2_card_lar,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v4_ordinal1 @ A ) & ~ ( v1_xboole_0 @ A ) ) => ( ( v3_ordinal1 @ A ) & ~ ( v1_finset_1 @ A ) ) ) ),file(card_lar,cc2_card_lar)).
thf(cc5_card_3,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v4_card_3 @ A ) ) => ( v5_card_3 @ A ) ) ),file(card_3,cc5_card_3)).
thf(cc7_card_3,axiom,( ! [A: $i] : ( ( v4_card_3 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_card_3 @ B ) ) ) ),file(card_3,cc7_card_3)).
thf(cc9_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ np__1 ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) ) ),file(card_1,cc9_card_1)).
thf(rc1_card_lar,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v4_ordinal1 @ A ) & ~ ( v1_xboole_0 @ A ) & ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ~ ( v4_card_3 @ A ) & ( v1_card_5 @ A ) ) ),file(card_lar,rc1_card_lar)).
thf(rc1_ordinal2,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v4_ordinal1 @ A ) ) ),file(ordinal2,rc1_ordinal2)).
thf(rc2_card_lar,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ~ ( v4_card_3 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ( v1_ordinal1 @ B ) & ( v2_ordinal1 @ B ) & ( v3_ordinal1 @ B ) & ~ ( v1_finset_1 @ B ) & ( v1_card_1 @ B ) ) ) ),file(card_lar,rc2_card_lar)).
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_card_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v3_card_1 @ B @ np__1 ) ) ) ),file(card_1,rc7_card_1)).
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(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(cc10_card_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) => ( v3_card_1 @ A @ np__1 ) ) ),file(card_1,cc10_card_1)).
thf(cc1_card_5,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(card_5,cc1_card_5)).
thf(cc1_card_lar,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) => ( ( v3_ordinal1 @ A ) & ( v4_ordinal1 @ A ) ) ) ),file(card_lar,cc1_card_lar)).
thf(cc3_card_lar,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ~ ( v2_card_1 @ A ) ) => ( ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ~ ( v4_card_3 @ A ) ) ) ),file(card_lar,cc3_card_lar)).
thf(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc4_card_3,axiom,( ! [A: $i] : ( ( v5_card_3 @ A ) => ( ~ ( v1_finset_1 @ A ) & ( v4_card_3 @ A ) ) ) ),file(card_3,cc4_card_3)).
thf(cc4_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_0)).
thf(cc5_subset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,cc5_subset_1)).
thf(cc6_card_1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) ) => ( v7_ordinal1 @ A ) ) ),file(card_1,cc6_card_1)).
thf(cc6_card_3,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v4_card_3 @ A ) ) ),file(card_3,cc6_card_3)).
thf(cc6_card_fil,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ~ ( v2_card_1 @ A ) ) => ( ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ( v1_card_5 @ A ) ) ) ),file(card_fil,cc6_card_fil)).
thf(cc6_funct_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc6_funct_1)).
thf(fc10_card_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_finset_1 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(card_1,fc10_card_1)).
thf(fc11_card_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_finset_1 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) ),file(card_1,fc11_card_1)).
thf(fc18_funct_1,axiom,( ! [A: $i] : ( ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(funct_1,fc18_funct_1)).
thf(fc24_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc24_relat_1)).
thf(fc9_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(card_1,fc9_card_1)).
thf(rc1_card_5,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(card_5,rc1_card_5)).
thf(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(rc2_card_1,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(card_1,rc2_card_1)).
thf(rc2_card_fil,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ~ ( v2_card_1 @ A ) ) ),file(card_fil,rc2_card_fil)).
thf(rc3_card_1,axiom,( ? [A: $i] : ~ ( v1_finset_1 @ A ) ),file(card_1,rc3_card_1)).
thf(rc4_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_finset_1 @ B ) ) ) ),file(card_1,rc4_card_1)).
thf(rc5_card_3,axiom,( ? [A: $i] : ( v5_card_3 @ A ) ),file(card_3,rc5_card_3)).
thf(rc5_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc5_subset_1)).
thf(rc6_card_3,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v1_finset_1 @ A ) ) ),file(card_3,rc6_card_3)).
thf(rc6_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,rc6_subset_1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(dt_k1_funct_2,axiom,( $true ),file(funct_2,k1_funct_2)).
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_k2_funct_7,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k2_funct_7 @ A @ B @ C ) ) & ( v1_funct_1 @ ( k2_funct_7 @ A @ B @ C ) ) ) ) ),file(funct_7,k2_funct_7)).
thf(dt_k3_card_3,axiom,( $true ),file(card_3,k3_card_3)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_m1_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_finseq_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) ) ),file(finseq_1,m1_finseq_1)).
thf(dt_m1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_funct_2 @ C @ A @ B ) => ~ ( v1_xboole_0 @ C ) ) ),file(funct_2,m1_funct_2)).
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_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(cc1_classes2,axiom,( ! [A: $i] : ( ( v2_classes1 @ A ) => ( v1_classes1 @ A ) ) ),file(classes2,cc1_classes2)).
thf(cc1_xreal_0,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k1_numbers ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc1_xreal_0)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
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(cc2_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
thf(cc3_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc3_card_1)).
thf(cc3_classes2,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_classes1 @ A ) ) => ( v1_classes2 @ A ) ) ),file(classes2,cc3_classes2)).
thf(cc4_card_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc4_card_1)).
thf(cc5_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc5_card_1)).
thf(cc5_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ) ),file(funct_1,cc5_funct_1)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc7_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ k1_xboole_0 ) => ( v1_xboole_0 @ A ) ) ),file(card_1,cc7_card_1)).
thf(cc7_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc7_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(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
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(fc10_card_3,axiom,( v5_card_3 @ k4_ordinal1 ),file(card_3,fc10_card_3)).
thf(fc14_card_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_card_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v3_card_1 @ B @ A ) ) => ( v3_card_1 @ ( k9_xtuple_0 @ B ) @ A ) ) ),file(card_1,fc14_card_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(fc19_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc19_funct_1)).
thf(fc1_card_5,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) & ( v1_ordinal2 @ A ) ) => ( v3_ordinal1 @ ( k3_card_3 @ A ) ) ) ),file(card_5,fc1_card_5)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc2_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(ordinal2,fc2_ordinal2)).
thf(fc4_card_1,axiom,( v1_card_1 @ k4_ordinal1 ),file(card_1,fc4_card_1)).
thf(fc4_zf_lang,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m1_finseq_1 @ A @ k5_numbers ) ) => ( v1_zf_lang @ ( k6_zf_lang @ A ) ) ) ),file(zf_lang,fc4_zf_lang)).
thf(fc5_card_1,axiom,( v2_card_1 @ k4_ordinal1 ),file(card_1,fc5_card_1)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(fc7_card_1,axiom,( ~ ( v1_finset_1 @ k4_ordinal1 ) ),file(card_1,fc7_card_1)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(rc1_card_3,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_card_3 @ A ) ) ),file(card_3,rc1_card_3)).
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_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ),file(funct_1,rc2_funct_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(rc2_ordinal2,axiom,( ? [A: $i] : ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) ),file(ordinal2,rc2_ordinal2)).
thf(rc2_ordinal4,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_classes2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ( v1_ordinal1 @ B ) & ( v2_ordinal1 @ B ) & ( v3_ordinal1 @ B ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(ordinal4,rc2_ordinal4)).
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(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_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
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(rc5_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( v3_card_1 @ B @ A ) ) ),file(card_1,rc5_card_1)).
thf(rc5_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) ),file(funct_1,rc5_funct_1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(rc6_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v3_card_1 @ B @ A ) ) ) ),file(card_1,rc6_card_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(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(rc9_funct_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) ),file(funct_1,rc9_funct_1)).
thf(reflexivity_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( r1_ordinal1 @ A @ A ) ) ),file(ordinal1,r1_ordinal1)).
thf(connectedness_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) | ( r1_ordinal1 @ B @ A ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k2_zf_lang1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ k1_zf_lang @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k1_zf_lang @ A ) ) ) & ( m1_subset_1 @ C @ k1_zf_lang ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k2_zf_lang1 @ A @ B @ C @ D ) @ ( k2_funct_7 @ B @ C @ D ) ) ) ),file(zf_lang1,k2_zf_lang1)).
thf(redefinition_k4_zf_refle,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_classes2 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_zf_refle @ B @ A ) ) => ( = @ ( k4_zf_refle @ A @ B ) @ ( k3_card_3 @ B ) ) ) ),file(zf_refle,k4_zf_refle)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_k9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( = @ ( k9_funct_2 @ A @ B ) @ ( k1_funct_2 @ A @ B ) ) ) ),file(funct_2,k9_funct_2)).
thf(redefinition_m2_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m2_finseq_1 @ B @ A ) <=> ( m1_finseq_1 @ B @ A ) ) ),file(finseq_1,m2_finseq_1)).
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(redefinition_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) <=> ( r1_tarski @ A @ B ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_zf_lang,axiom,( m1_subset_1 @ k1_zf_lang @ ( k1_zfmisc_1 @ k5_numbers ) ),file(zf_lang,k1_zf_lang)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k23_zf_lang,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m1_finseq_1 @ A @ k5_numbers ) ) => ( m2_subset_1 @ ( k23_zf_lang @ A ) @ k5_numbers @ k1_zf_lang ) ) ),file(zf_lang,k23_zf_lang)).
thf(dt_k24_zf_lang,axiom,( ! [A: $i] : ( ( ( v1_zf_lang @ A ) & ( m1_finseq_1 @ A @ k5_numbers ) ) => ( ( v1_zf_lang @ ( k24_zf_lang @ A ) ) & ( m2_finseq_1 @ ( k24_zf_lang @ A ) @ k5_numbers ) ) ) ),file(zf_lang,k24_zf_lang)).
thf(dt_k2_ordinal4,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_classes2 @ A ) ) => ( ( v3_ordinal1 @ ( k2_ordinal4 @ A ) ) & ( m1_subset_1 @ ( k2_ordinal4 @ A ) @ A ) ) ) ),file(ordinal4,k2_ordinal4)).
thf(dt_k2_zf_lang1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ k1_zf_lang @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k1_zf_lang @ A ) ) ) & ( m1_subset_1 @ C @ k1_zf_lang ) & ( m1_subset_1 @ D @ A ) ) => ( ( v1_funct_1 @ ( k2_zf_lang1 @ A @ B @ C @ D ) ) & ( v1_funct_2 @ ( k2_zf_lang1 @ A @ B @ C @ D ) @ k1_zf_lang @ A ) & ( m1_subset_1 @ ( k2_zf_lang1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k1_zf_lang @ A ) ) ) ) ) ),file(zf_lang1,k2_zf_lang1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k4_zf_refle,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_classes2 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_zf_refle @ B @ A ) ) => ( ~ ( v1_xboole_0 @ ( k4_zf_refle @ A @ B ) ) & ( m1_subset_1 @ ( k4_zf_refle @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),file(zf_refle,k4_zf_refle)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k6_zf_lang,axiom,( ! [A: $i] : ( ( m1_finseq_1 @ A @ k5_numbers ) => ( m2_finseq_1 @ ( k6_zf_lang @ A ) @ k5_numbers ) ) ),file(zf_lang,k6_zf_lang)).
thf(dt_k9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( m1_funct_2 @ ( k9_funct_2 @ A @ B ) @ A @ B ) ) ),file(funct_2,k9_funct_2)).
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_m2_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m2_finseq_1 @ B @ A ) => ( ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) ) ) ),file(finseq_1,m2_finseq_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(dt_c1_30__zf_refle,axiom,( ~ ( v1_xboole_0 @ c1_30__zf_refle ) & ( v1_classes2 @ c1_30__zf_refle ) ),file(zf_refle,c1_30__zf_refle)).
thf(dt_c1_30_1__zf_refle,axiom,( ( v1_zf_lang @ c1_30_1__zf_refle ) & ( m2_finseq_1 @ c1_30_1__zf_refle @ k5_numbers ) ),file(zf_refle,c1_30_1__zf_refle)).
thf(dt_c2_30__zf_refle,axiom,( ( v1_relat_1 @ c2_30__zf_refle ) & ( v2_relat_1 @ c2_30__zf_refle ) & ( v5_relat_1 @ c2_30__zf_refle @ c1_30__zf_refle ) & ( v5_ordinal1 @ c2_30__zf_refle ) & ( v1_funct_1 @ c2_30__zf_refle ) & ( v1_zf_refle @ c2_30__zf_refle @ c1_30__zf_refle ) ),file(zf_refle,c2_30__zf_refle)).
thf(cc1_card_3,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_card_3 @ A ) ) ) ),file(card_3,cc1_card_3)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc1_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( ( v5_ordinal1 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( ( v5_ordinal1 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_ordinal2 @ B ) ) ) ) ),file(ordinal2,cc1_ordinal2)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_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(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_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc2_card_1)).
thf(cc2_classes2,axiom,( ! [A: $i] : ( ( v1_classes2 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_classes1 @ A ) ) ) ),file(classes2,cc2_classes2)).
thf(cc2_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) ) ) ),file(funct_1,cc2_funct_1)).
thf(cc2_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal2,cc2_ordinal2)).
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(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc3_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) ) ),file(relat_1,cc3_relat_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_funct_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) ) ),file(funct_1,cc4_funct_1)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc4_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ) ),file(relat_1,cc4_relat_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(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
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(cc7_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc8_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_card_1 @ A @ k1_xboole_0 ) ) ),file(card_1,cc8_card_1)).
thf(cc8_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc8_relat_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc10_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc10_relat_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(fc11_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( m1_subset_1 @ B @ ( k9_xtuple_0 @ A ) ) ) => ~ ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc11_funct_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc1_zf_lang,axiom,( ~ ( v1_xboole_0 @ k1_zf_lang ) ),file(zf_lang,fc1_zf_lang)).
thf(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
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_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc8_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_classes2,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_classes2 @ A ) ) ),file(classes2,rc1_classes2)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_ordinal4,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_classes2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ( v3_ordinal1 @ B ) ) ) ),file(ordinal4,rc1_ordinal4)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_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(rc1_zf_refle,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_classes2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(zf_refle,rc1_zf_refle)).
thf(rc2_classes2,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_classes2 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ~ ( v1_xboole_0 @ B ) ) ) ),file(classes2,rc2_classes2)).
thf(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
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(rc2_zf_refle,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_classes2 @ A ) ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v5_ordinal1 @ B ) & ( v1_funct_1 @ B ) & ( v1_zf_refle @ B @ A ) ) ) ),file(zf_refle,rc2_zf_refle)).
thf(rc3_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc3_funct_1)).
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_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc4_funct_1)).
thf(e3_30_1__zf_refle,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k9_funct_2 @ k1_zf_lang @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) ) => ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( m1_subset_1 @ B @ c1_30__zf_refle ) & ? [C: $i] : ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ k1_zf_lang @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k1_zf_lang @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) ) ) & ( = @ A @ C ) & ~ ( ! [D: $i] : ( ( m2_subset_1 @ D @ c1_30__zf_refle @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) => ~ ( ( r2_hidden @ D @ ( k1_funct_1 @ c2_30__zf_refle @ B ) ) & ( r1_zf_model @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ ( k2_zf_lang1 @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ C @ ( k23_zf_lang @ c1_30_1__zf_refle ) @ D ) @ ( k6_zf_lang @ ( k24_zf_lang @ c1_30_1__zf_refle ) ) ) ) ) & ~ ( ( = @ B @ ( k2_ordinal4 @ c1_30__zf_refle ) ) & ! [D: $i] : ( ( m2_subset_1 @ D @ c1_30__zf_refle @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) => ~ ( r1_zf_model @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ ( k2_zf_lang1 @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ C @ ( k23_zf_lang @ c1_30_1__zf_refle ) @ D ) @ ( k6_zf_lang @ ( k24_zf_lang @ c1_30_1__zf_refle ) ) ) ) ) ) ) ) ) ),file(zf_refle,e3_30_1__zf_refle)).
thf(s1_zf_refle,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ C ) & ( v1_classes2 @ C ) & ~ ( v1_xboole_0 @ B ) ) => ( ! [D: $i] : ( ( m1_subset_1 @ D @ B ) => ? [E: $i] : ( ( v3_ordinal1 @ E ) & ( m1_subset_1 @ E @ C ) & ( A @ D @ E ) ) ) => ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ ( k9_xtuple_0 @ D ) @ B ) & ! [E: $i] : ( ( m1_subset_1 @ E @ B ) => ? [F: $i] : ( ( v3_ordinal1 @ F ) & ( m1_subset_1 @ F @ C ) & ( = @ F @ ( k1_funct_1 @ D @ E ) ) & ( A @ E @ F ) & ! [G: $i] : ( ( ( v3_ordinal1 @ G ) & ( m1_subset_1 @ G @ C ) ) => ( ( A @ E @ G ) => ( r1_ordinal1 @ F @ G ) ) ) ) ) ) ) ) ),file(zf_refle,s1_zf_refle)).
thf(e4_30_1__zf_refle,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k9_funct_2 @ k1_zf_lang @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_funct_2 @ k1_zf_lang @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) ) => ? [C: $i] : ( ( v3_ordinal1 @ C ) & ( m1_subset_1 @ C @ c1_30__zf_refle ) & ( = @ C @ ( k1_funct_1 @ A @ B ) ) & ? [D: $i] : ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ k1_zf_lang @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k1_zf_lang @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) ) ) & ( = @ B @ D ) & ~ ( ! [E: $i] : ( ( m2_subset_1 @ E @ c1_30__zf_refle @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) => ~ ( ( r2_hidden @ E @ ( k1_funct_1 @ c2_30__zf_refle @ C ) ) & ( r1_zf_model @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ ( k2_zf_lang1 @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ D @ ( k23_zf_lang @ c1_30_1__zf_refle ) @ E ) @ ( k6_zf_lang @ ( k24_zf_lang @ c1_30_1__zf_refle ) ) ) ) ) & ~ ( ( = @ C @ ( k2_ordinal4 @ c1_30__zf_refle ) ) & ! [E: $i] : ( ( m2_subset_1 @ E @ c1_30__zf_refle @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) => ~ ( r1_zf_model @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ ( k2_zf_lang1 @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ D @ ( k23_zf_lang @ c1_30_1__zf_refle ) @ E ) @ ( k6_zf_lang @ ( k24_zf_lang @ c1_30_1__zf_refle ) ) ) ) ) ) ) & ! [D: $i] : ( ( ( v3_ordinal1 @ D ) & ( m1_subset_1 @ D @ c1_30__zf_refle ) ) => ( ? [E: $i] : ( ( v1_funct_1 @ E ) & ( v1_funct_2 @ E @ k1_zf_lang @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k1_zf_lang @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) ) ) & ( = @ B @ E ) & ~ ( ! [F: $i] : ( ( m2_subset_1 @ F @ c1_30__zf_refle @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) => ~ ( ( r2_hidden @ F @ ( k1_funct_1 @ c2_30__zf_refle @ D ) ) & ( r1_zf_model @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ ( k2_zf_lang1 @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ E @ ( k23_zf_lang @ c1_30_1__zf_refle ) @ F ) @ ( k6_zf_lang @ ( k24_zf_lang @ c1_30_1__zf_refle ) ) ) ) ) & ~ ( ( = @ D @ ( k2_ordinal4 @ c1_30__zf_refle ) ) & ! [F: $i] : ( ( m2_subset_1 @ F @ c1_30__zf_refle @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) ) => ~ ( r1_zf_model @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ ( k2_zf_lang1 @ ( k4_zf_refle @ c1_30__zf_refle @ c2_30__zf_refle ) @ E @ ( k23_zf_lang @ c1_30_1__zf_refle ) @ F ) @ ( k6_zf_lang @ ( k24_zf_lang @ c1_30_1__zf_refle ) ) ) ) ) ) ) => ( r1_ordinal1 @ C @ D ) ) ) ) ) ) ),file(zf_refle,e4_30_1__zf_refle)).
