% Mizar problem: e2_112,sublemma,2878,30 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_112_type,type,( c1_112__sublemma: $i )).
thf(c2_112_type,type,( c2_112__sublemma: $i )).
thf(c3_112_type,type,( c3_112__sublemma: $i )).
thf(k16_substut1_type,type,( k16_substut1: $i > $i )).
thf(k17_substut1_type,type,( k17_substut1: $i > $i > $i > $i > $i )).
thf(k19_substut1_type,type,( k19_substut1: $i > $i > $i )).
thf(k1_funct_4_type,type,( k1_funct_4: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_sublemma_type,type,( k1_sublemma: $i > $i > $i > $i > $i )).
thf(k1_substut1_type,type,( k1_substut1: $i > $i )).
thf(k1_valuat_1_type,type,( k1_valuat_1: $i > $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k20_substut1_type,type,( k20_substut1: $i > $i > $i )).
thf(k2_qc_lang1_type,type,( k2_qc_lang1: $i > $i )).
thf(k2_valuat_1_type,type,( k2_valuat_1: $i > $i > $i )).
thf(k2_xtuple_0_type,type,( k2_xtuple_0: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k37_substut1_type,type,( k37_substut1: $i > $i > $i )).
thf(k38_substut1_type,type,( k38_substut1: $i > $i )).
thf(k39_substut1_type,type,( k39_substut1: $i > $i > $i )).
thf(k3_cqc_lang_type,type,( k3_cqc_lang: $i > $i )).
thf(k3_margrel1_type,type,( k3_margrel1: $i > $i )).
thf(k3_qc_lang1_type,type,( k3_qc_lang1: $i > $i )).
thf(k3_sublemma_type,type,( k3_sublemma: $i > $i > $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k4_sublemma_type,type,( k4_sublemma: $i > $i > $i > $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k5_sublemma_type,type,( k5_sublemma: $i > $i > $i )).
thf(k6_qc_lang1_type,type,( k6_qc_lang1: $i > $i )).
thf(k6_sublemma_type,type,( k6_sublemma: $i > $i > $i > $i )).
thf(k7_sublemma_type,type,( k7_sublemma: $i > $i > $i > $i )).
thf(k8_qc_lang1_type,type,( k8_qc_lang1: $i > $i > $i )).
thf(k9_qc_lang1_type,type,( k9_qc_lang1: $i > $i )).
thf(k9_sublemma_type,type,( k9_sublemma: $i > $i > $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_qc_lang1_type,type,( m1_qc_lang1: $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m1_substut1_type,type,( m1_substut1: $i > $i > $i > $o )).
thf(m1_valuat_1_type,type,( m1_valuat_1: $i > $i > $i > $o )).
thf(m2_finseq_1_type,type,( m2_finseq_1: $i > $i > $o )).
thf(m2_funct_2_type,type,( m2_funct_2: $i > $i > $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(r1_sublemma_type,type,( r1_sublemma: $i > $i > $i > $i > $i > $o )).
thf(r1_valuat_1_type,type,( r1_valuat_1: $i > $i > $i > $i > $i > $o )).
thf(v1_card_1_type,type,( v1_card_1: $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_funcop_1_type,type,( v1_funcop_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_membered_type,type,( v1_membered: $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_sublemma_type,type,( v1_sublemma: $i > $i > $o )).
thf(v1_subset_1_type,type,( v1_subset_1: $i > $i > $o )).
thf(v1_substut1_type,type,( v1_substut1: $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_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v1_xxreal_2_type,type,( v1_xxreal_2: $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_funcop_1_type,type,( v2_funcop_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_membered_type,type,( v2_membered: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_substut1_type,type,( v2_substut1: $i > $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v2_xxreal_2_type,type,( v2_xxreal_2: $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_membered_type,type,( v3_membered: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v3_substut1_type,type,( v3_substut1: $i > $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v3_xxreal_2_type,type,( v3_xxreal_2: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v4_substut1_type,type,( v4_substut1: $i > $i > $o )).
thf(v4_xxreal_2_type,type,( v4_xxreal_2: $i > $o )).
thf(v5_membered_type,type,( v5_membered: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_substut1_type,type,( v5_substut1: $i > $i > $o )).
thf(v5_xxreal_2_type,type,( v5_xxreal_2: $i > $o )).
thf(v6_membered_type,type,( v6_membered: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v6_xxreal_2_type,type,( v6_xxreal_2: $i > $o )).
thf(v7_membered_type,type,( v7_membered: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
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(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(cc11_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v3_membered @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc11_xxreal_2)).
thf(cc12_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xcmplx_0 @ B ) ) ) ),file(membered,cc12_membered)).
thf(cc12_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ( v1_finset_1 @ A ) ) ) ),file(xxreal_2,cc12_xxreal_2)).
thf(cc13_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xxreal_0 @ B ) ) ) ),file(membered,cc13_membered)).
thf(cc14_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v3_membered @ A ) ) ) ),file(xxreal_2,cc14_xxreal_2)).
thf(cc15_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_rat_1 @ B ) ) ) ),file(membered,cc15_membered)).
thf(cc15_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v2_membered @ A ) & ( v6_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc15_xxreal_2)).
thf(cc16_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) ) ),file(xxreal_2,cc16_xxreal_2)).
thf(cc17_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v2_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) ) ),file(xxreal_2,cc17_xxreal_2)).
thf(cc19_membered,axiom,( ! [A: $i] : ( ( v1_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_membered @ B ) ) ) ),file(membered,cc19_membered)).
thf(cc20_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_membered @ B ) ) ) ),file(membered,cc20_membered)).
thf(cc22_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_membered @ B ) ) ) ),file(membered,cc22_membered)).
thf(cc2_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) => ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc2_xxreal_2)).
thf(cc3_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
thf(cc3_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc3_xxreal_0)).
thf(cc4_xxreal_0,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc4_xxreal_0)).
thf(cc4_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v3_xxreal_2 @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc4_xxreal_2)).
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(cc5_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) => ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc5_xxreal_0)).
thf(cc5_xxreal_2,axiom,( ! [A: $i] : ( ( ( v2_membered @ A ) & ( v3_xxreal_2 @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v2_membered @ A ) & ( v5_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc5_xxreal_2)).
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(cc6_xxreal_0,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc6_xxreal_0)).
thf(cc8_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) => ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc8_xxreal_0)).
thf(rc1_xxreal_2,axiom,( ? [A: $i] : ( ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v4_membered @ A ) & ( v5_membered @ A ) & ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) ) ),file(xxreal_2,rc1_xxreal_2)).
thf(rc2_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ),file(xxreal_0,rc2_xxreal_0)).
thf(rc3_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ),file(xxreal_0,rc3_xxreal_0)).
thf(rc3_xxreal_2,axiom,( ? [A: $i] : ( ( v1_membered @ A ) & ( v2_membered @ A ) & ( v3_membered @ A ) & ( v4_membered @ A ) & ( v5_membered @ A ) & ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) & ( v5_xxreal_2 @ A ) ) ),file(xxreal_2,rc3_xxreal_2)).
thf(rc4_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc4_xxreal_2)).
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(rc5_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc5_xxreal_2)).
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(rc6_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xxreal_2 @ A ) & ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc6_xxreal_2)).
thf(rc7_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ( v1_xxreal_2 @ A ) & ~ ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc7_xxreal_2)).
thf(rc8_xxreal_2,axiom,( ? [A: $i] : ( ( v2_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ~ ( v1_xxreal_2 @ A ) & ~ ( v2_xxreal_2 @ A ) & ( v6_xxreal_2 @ A ) ) ),file(xxreal_2,rc8_xxreal_2)).
thf(cc10_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v1_xxreal_2 @ A ) ) => ( ( v3_membered @ A ) & ( v3_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc10_xxreal_2)).
thf(cc13_xxreal_2,axiom,( ! [A: $i] : ( ( ( v6_membered @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v6_membered @ A ) & ( v1_finset_1 @ A ) & ( v4_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc13_xxreal_2)).
thf(cc14_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(membered,cc14_membered)).
thf(cc16_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_int_1 @ B ) ) ) ),file(membered,cc16_membered)).
thf(cc21_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_membered @ B ) ) ) ),file(membered,cc21_membered)).
thf(cc23_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_membered @ B ) ) ) ),file(membered,cc23_membered)).
thf(cc2_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funcop_1 @ A ) ) ) ),file(funcop_1,cc2_funcop_1)).
thf(cc2_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ( v4_membered @ A ) ) ),file(membered,cc2_membered)).
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(cc4_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
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_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v1_membered @ A ) ) ),file(membered,cc5_membered)).
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_card_1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) ) => ( v7_ordinal1 @ A ) ) ),file(card_1,cc6_card_1)).
thf(cc6_xxreal_2,axiom,( ! [A: $i] : ( ( ( v3_membered @ A ) & ( v1_finset_1 @ A ) ) => ( ( v3_membered @ A ) & ( v5_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc6_xxreal_2)).
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(cc7_xxreal_0,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) => ( ( v1_xxreal_0 @ A ) & ~ ( v2_xxreal_0 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(xxreal_0,cc7_xxreal_0)).
thf(cc7_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v4_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v2_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc7_xxreal_2)).
thf(cc8_xxreal_2,axiom,( ! [A: $i] : ( ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v3_xxreal_2 @ A ) ) => ( ( v5_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc8_xxreal_2)).
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(fc5_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k1_funct_4 @ A @ B ) ) & ( v2_relat_1 @ ( k1_funct_4 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_4 @ A @ B ) ) ) ) ),file(funct_4,fc5_funct_4)).
thf(fc6_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_funcop_1 @ B ) ) => ( ( v1_relat_1 @ ( k1_funct_4 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_4 @ A @ B ) ) & ( v1_funcop_1 @ ( k1_funct_4 @ A @ B ) ) ) ) ),file(funct_4,fc6_funct_4)).
thf(fc7_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) ) => ( ( v1_relat_1 @ ( k1_funct_4 @ B @ C ) ) & ( v4_relat_1 @ ( k1_funct_4 @ B @ C ) @ A ) & ( v1_funct_1 @ ( k1_funct_4 @ B @ C ) ) ) ) ),file(funct_4,fc7_funct_4)).
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_cqc_lang,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ? [C: $i] : ( ( m1_finseq_1 @ C @ ( k2_qc_lang1 @ A ) ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ k5_numbers ) & ( v5_relat_1 @ C @ ( k2_qc_lang1 @ A ) ) & ( v5_relat_1 @ C @ ( k3_qc_lang1 @ A ) ) & ( v1_funct_1 @ C ) & ( v3_card_1 @ C @ B ) & ( v1_finseq_1 @ C ) ) ) ),file(cqc_lang,rc1_cqc_lang)).
thf(rc1_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ),file(funcop_1,rc1_funcop_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(rc1_substut1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_substut1 @ A ) ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(substut1,rc1_substut1)).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(rc1_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_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_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) ) ),file(funcop_1,rc2_funcop_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_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc2_xxreal_2,axiom,( ? [A: $i] : ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(xxreal_2,rc2_xxreal_2)).
thf(rc3_card_1,axiom,( ? [A: $i] : ~ ( v1_finset_1 @ A ) ),file(card_1,rc3_card_1)).
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_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_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(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(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(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
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(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(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(idempotence_k1_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( = @ ( k1_funct_4 @ A @ A ) @ A ) ) ),file(funct_4,k1_funct_4)).
thf(dt_k17_substut1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k6_qc_lang1 @ A ) ) & ( m1_finseq_1 @ C @ ( k2_qc_lang1 @ A ) ) & ( m1_subset_1 @ D @ ( k1_substut1 @ A ) ) ) => ( m1_subset_1 @ ( k17_substut1 @ A @ B @ C @ D ) @ ( k16_substut1 @ A ) ) ) ),file(substut1,k17_substut1)).
thf(dt_k1_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k1_funct_4 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_4 @ A @ B ) ) ) ) ),file(funct_4,k1_funct_4)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_valuat_1,axiom,( $true ),file(valuat_1,k1_valuat_1)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k20_substut1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k16_substut1 @ A ) ) ) => ( m1_subset_1 @ ( k20_substut1 @ A @ B ) @ ( k16_substut1 @ A ) ) ) ),file(substut1,k20_substut1)).
thf(dt_k2_xtuple_0,axiom,( $true ),file(xtuple_0,k2_xtuple_0)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k37_substut1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k16_substut1 @ A ) ) ) => ( m1_subset_1 @ ( k37_substut1 @ A @ B ) @ ( k9_qc_lang1 @ A ) ) ) ),file(substut1,k37_substut1)).
thf(dt_k3_cqc_lang,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( m1_subset_1 @ ( k3_cqc_lang @ A ) @ ( k1_zfmisc_1 @ ( k9_qc_lang1 @ A ) ) ) ) ),file(cqc_lang,k3_cqc_lang)).
thf(dt_k3_margrel1,axiom,( $true ),file(margrel1,k3_margrel1)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_k9_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k9_qc_lang1)).
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(cc11_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k5_numbers ) ) => ( v6_membered @ A ) ) ),file(membered,cc11_membered)).
thf(cc17_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v7_ordinal1 @ B ) ) ) ),file(membered,cc17_membered)).
thf(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(cc1_funcop_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_funcop_1 @ B ) ) ) ) ),file(funcop_1,cc1_funcop_1)).
thf(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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(cc24_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_membered @ B ) ) ) ),file(membered,cc24_membered)).
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_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(cc2_xxreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,cc2_xxreal_0)).
thf(cc3_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc3_card_1)).
thf(cc3_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ) ),file(funcop_1,cc3_funcop_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_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(cc3_xxreal_2,axiom,( ! [A: $i] : ( ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) ) => ( ( v6_membered @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc3_xxreal_2)).
thf(cc4_card_1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc4_card_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_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_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc5_card_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(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_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ k1_xboole_0 ) => ( v1_xboole_0 @ A ) ) ),file(card_1,cc7_card_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_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) => ( v3_membered @ A ) ) ),file(membered,cc8_membered)).
thf(cc8_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
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_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(cc9_xxreal_2,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( ( v6_membered @ A ) & ( v3_xxreal_2 @ A ) ) ) ),file(xxreal_2,cc9_xxreal_2)).
thf(fc10_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) ) => ( ( v1_relat_1 @ ( k1_funct_4 @ B @ C ) ) & ( v5_relat_1 @ ( k1_funct_4 @ B @ C ) @ A ) & ( v1_funct_1 @ ( k1_funct_4 @ B @ C ) ) ) ) ),file(funct_4,fc10_funct_4)).
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_xxreal_2,axiom,( ~ ( v3_xxreal_2 @ k1_numbers ) & ~ ( v4_xxreal_2 @ k1_numbers ) ),file(xxreal_2,fc11_xxreal_2)).
thf(fc17_xxreal_2,axiom,( v6_xxreal_2 @ k1_numbers ),file(xxreal_2,fc17_xxreal_2)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc2_cqc_lang,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k3_cqc_lang @ A ) ) ) ),file(cqc_lang,fc2_cqc_lang)).
thf(fc3_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ~ ( v1_xboole_0 @ B ) ) => ( ( v1_relat_1 @ ( k1_funct_4 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_4 @ A @ B ) ) & ~ ( v1_xboole_0 @ ( k1_funct_4 @ A @ B ) ) ) ) ),file(funct_4,fc3_funct_4)).
thf(fc3_membered,axiom,( v3_membered @ k1_numbers ),file(membered,fc3_membered)).
thf(fc4_card_1,axiom,( v1_card_1 @ k4_ordinal1 ),file(card_1,fc4_card_1)).
thf(fc4_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ~ ( v1_xboole_0 @ B ) ) => ( ( v1_relat_1 @ ( k1_funct_4 @ B @ A ) ) & ( v1_funct_1 @ ( k1_funct_4 @ B @ A ) ) & ~ ( v1_xboole_0 @ ( k1_funct_4 @ B @ A ) ) ) ) ),file(funct_4,fc4_funct_4)).
thf(fc56_membered,axiom,( v7_membered @ k1_numbers ),file(membered,fc56_membered)).
thf(fc59_membered,axiom,( v7_membered @ k4_ordinal1 ),file(membered,fc59_membered)).
thf(fc5_card_1,axiom,( v2_card_1 @ k4_ordinal1 ),file(card_1,fc5_card_1)).
thf(fc5_substut1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) & ( m1_subset_1 @ C @ ( k8_qc_lang1 @ A @ B ) ) & ( v3_card_1 @ D @ B ) & ( m1_finseq_1 @ D @ ( k2_qc_lang1 @ A ) ) & ( m1_subset_1 @ E @ ( k1_substut1 @ A ) ) ) => ( v4_substut1 @ ( k17_substut1 @ A @ C @ D @ E ) @ A ) ) ),file(substut1,fc5_substut1)).
thf(fc6_membered,axiom,( v6_membered @ k4_ordinal1 ),file(membered,fc6_membered)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_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(fc6_substut1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k16_substut1 @ A ) ) ) => ( v5_substut1 @ ( k20_substut1 @ A @ B ) @ A ) ) ),file(substut1,fc6_substut1)).
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_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc1_membered)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(rc1_sublemma,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k2_zfmisc_1 @ ( k16_substut1 @ A ) @ ( k3_qc_lang1 @ A ) ) ) & ( v1_sublemma @ B @ A ) ) ) ),file(sublemma,rc1_sublemma)).
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(rc2_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc2_membered)).
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_substut1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ? [B: $i] : ( ~ ( v1_xboole_0 @ B ) & ( v1_substut1 @ B @ A ) ) ) ),file(substut1,rc2_substut1)).
thf(rc3_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) & ( v7_membered @ A ) ) ),file(membered,rc3_membered)).
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_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( v3_card_1 @ B @ A ) ) ),file(card_1,rc5_card_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(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(rd1_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_xboole_0 @ B ) ) => ( = @ ( k1_funct_4 @ B @ A ) @ A ) ) ),file(funct_4,rd1_funct_4)).
thf(rd2_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_xboole_0 @ B ) ) => ( = @ ( k1_funct_4 @ A @ B ) @ A ) ) ),file(funct_4,rd2_funct_4)).
thf(rd2_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xtuple_0 @ ( k4_tarski @ A @ B ) ) @ B ) ),file(xtuple_0,rd2_xtuple_0)).
thf(rd3_funct_4,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( = @ ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ B ) @ ( k1_funct_4 @ A @ B ) ) ) ),file(funct_4,rd3_funct_4)).
thf(idempotence_k1_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_qc_lang1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ ( k2_valuat_1 @ A @ B ) ) & ( v1_funct_1 @ D ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k3_qc_lang1 @ A ) @ B ) ) ) ) => ( = @ ( k1_sublemma @ A @ B @ C @ C ) @ C ) ) ),file(sublemma,k1_sublemma)).
thf(redefinition_k19_substut1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k16_substut1 @ A ) ) ) => ( = @ ( k19_substut1 @ A @ B ) @ ( k2_xtuple_0 @ B ) ) ) ),file(substut1,k19_substut1)).
thf(redefinition_k1_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_qc_lang1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ ( k2_valuat_1 @ A @ B ) ) & ( v1_funct_1 @ D ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k3_qc_lang1 @ A ) @ B ) ) ) ) => ( = @ ( k1_sublemma @ A @ B @ C @ D ) @ ( k1_funct_4 @ C @ D ) ) ) ),file(sublemma,k1_sublemma)).
thf(redefinition_k2_valuat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ( = @ ( k2_valuat_1 @ A @ B ) @ ( k1_valuat_1 @ A @ B ) ) ) ),file(valuat_1,k2_valuat_1)).
thf(redefinition_k39_substut1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k38_substut1 @ A ) ) ) => ( = @ ( k39_substut1 @ A @ B ) @ ( k37_substut1 @ A @ B ) ) ) ),file(substut1,k39_substut1)).
thf(redefinition_k4_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( m1_qc_lang1 @ B ) & ( m1_subset_1 @ C @ ( k8_qc_lang1 @ B @ A ) ) & ( v5_relat_1 @ D @ ( k3_qc_lang1 @ B ) ) & ( v3_card_1 @ D @ A ) & ( m1_finseq_1 @ D @ ( k2_qc_lang1 @ B ) ) & ( m1_subset_1 @ E @ ( k1_substut1 @ B ) ) ) => ( = @ ( k4_sublemma @ A @ B @ C @ D @ E ) @ ( k17_substut1 @ B @ C @ D @ E ) ) ) ),file(sublemma,k4_sublemma)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_k5_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k38_substut1 @ A ) ) ) => ( = @ ( k5_sublemma @ A @ B ) @ ( k20_substut1 @ A @ B ) ) ) ),file(sublemma,k5_sublemma)).
thf(redefinition_k7_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k38_substut1 @ A ) ) & ( m1_subset_1 @ C @ ( k3_qc_lang1 @ A ) ) ) => ( = @ ( k7_sublemma @ A @ B @ C ) @ ( k4_tarski @ B @ C ) ) ) ),file(sublemma,k7_sublemma)).
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_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( m1_funct_2 @ C @ A @ B ) ) => ! [D: $i] : ( ( m2_funct_2 @ D @ A @ B @ C ) <=> ( m1_subset_1 @ D @ C ) ) ) ),file(funct_2,m2_funct_2)).
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(dt_k16_substut1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k16_substut1 @ A ) ) ) ),file(substut1,k16_substut1)).
thf(dt_k19_substut1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k16_substut1 @ A ) ) ) => ( m1_subset_1 @ ( k19_substut1 @ A @ B ) @ ( k1_substut1 @ A ) ) ) ),file(substut1,k19_substut1)).
thf(dt_k1_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_qc_lang1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ C @ ( k2_valuat_1 @ A @ B ) ) & ( v1_funct_1 @ D ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k3_qc_lang1 @ A ) @ B ) ) ) ) => ( m2_funct_2 @ ( k1_sublemma @ A @ B @ C @ D ) @ ( k3_qc_lang1 @ A ) @ B @ ( k2_valuat_1 @ A @ B ) ) ) ),file(sublemma,k1_sublemma)).
thf(dt_k1_substut1,axiom,( $true ),file(substut1,k1_substut1)).
thf(dt_k2_qc_lang1,axiom,( $true ),file(qc_lang1,k2_qc_lang1)).
thf(dt_k2_valuat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ( m1_funct_2 @ ( k2_valuat_1 @ A @ B ) @ ( k3_qc_lang1 @ A ) @ B ) ) ),file(valuat_1,k2_valuat_1)).
thf(dt_k38_substut1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( m1_subset_1 @ ( k38_substut1 @ A ) @ ( k1_zfmisc_1 @ ( k16_substut1 @ A ) ) ) ) ),file(substut1,k38_substut1)).
thf(dt_k39_substut1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k38_substut1 @ A ) ) ) => ( m2_subset_1 @ ( k39_substut1 @ A @ B ) @ ( k9_qc_lang1 @ A ) @ ( k3_cqc_lang @ A ) ) ) ),file(substut1,k39_substut1)).
thf(dt_k3_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( m1_subset_1 @ ( k3_qc_lang1 @ A ) @ ( k1_zfmisc_1 @ ( k2_qc_lang1 @ A ) ) ) ) ),file(qc_lang1,k3_qc_lang1)).
thf(dt_k3_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k38_substut1 @ A ) ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ D @ ( k2_valuat_1 @ A @ C ) ) ) => ( ( v1_funct_1 @ ( k3_sublemma @ A @ B @ C @ D ) ) & ( m1_subset_1 @ ( k3_sublemma @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k3_qc_lang1 @ A ) @ C ) ) ) ) ) ),file(sublemma,k3_sublemma)).
thf(dt_k4_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( m1_qc_lang1 @ B ) & ( m1_subset_1 @ C @ ( k8_qc_lang1 @ B @ A ) ) & ( v5_relat_1 @ D @ ( k3_qc_lang1 @ B ) ) & ( v3_card_1 @ D @ A ) & ( m1_finseq_1 @ D @ ( k2_qc_lang1 @ B ) ) & ( m1_subset_1 @ E @ ( k1_substut1 @ B ) ) ) => ( m2_subset_1 @ ( k4_sublemma @ A @ B @ C @ D @ E ) @ ( k16_substut1 @ B ) @ ( k38_substut1 @ B ) ) ) ),file(sublemma,k4_sublemma)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k5_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k38_substut1 @ A ) ) ) => ( m2_subset_1 @ ( k5_sublemma @ A @ B ) @ ( k16_substut1 @ A ) @ ( k38_substut1 @ A ) ) ) ),file(sublemma,k5_sublemma)).
thf(dt_k6_qc_lang1,axiom,( $true ),file(qc_lang1,k6_qc_lang1)).
thf(dt_k6_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k38_substut1 @ A ) ) & ( m1_subset_1 @ C @ ( k38_substut1 @ A ) ) ) => ( m2_subset_1 @ ( k6_sublemma @ A @ B @ C ) @ ( k16_substut1 @ A ) @ ( k38_substut1 @ A ) ) ) ),file(sublemma,k6_sublemma)).
thf(dt_k7_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k38_substut1 @ A ) ) & ( m1_subset_1 @ C @ ( k3_qc_lang1 @ A ) ) ) => ( ( v1_sublemma @ ( k7_sublemma @ A @ B @ C ) @ A ) & ( m1_subset_1 @ ( k7_sublemma @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k16_substut1 @ A ) @ ( k3_qc_lang1 @ A ) ) ) ) ) ),file(sublemma,k7_sublemma)).
thf(dt_k8_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ k5_numbers ) ) => ( m1_subset_1 @ ( k8_qc_lang1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k6_qc_lang1 @ A ) ) ) ) ),file(qc_lang1,k8_qc_lang1)).
thf(dt_k9_sublemma,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( v1_sublemma @ B @ A ) & ( m1_subset_1 @ B @ ( k2_zfmisc_1 @ ( k16_substut1 @ A ) @ ( k3_qc_lang1 @ A ) ) ) & ( m1_substut1 @ C @ A @ B ) ) => ( m2_subset_1 @ ( k9_sublemma @ A @ B @ C ) @ ( k16_substut1 @ A ) @ ( k38_substut1 @ A ) ) ) ),file(sublemma,k9_sublemma)).
thf(dt_m1_qc_lang1,axiom,( $true ),file(qc_lang1,m1_qc_lang1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_m1_substut1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k2_zfmisc_1 @ ( k16_substut1 @ A ) @ ( k3_qc_lang1 @ A ) ) ) ) => ! [C: $i] : ( ( m1_substut1 @ C @ A @ B ) => ( m1_subset_1 @ C @ ( k1_substut1 @ A ) ) ) ) ),file(substut1,m1_substut1)).
thf(dt_m1_valuat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ! [C: $i] : ( ( m1_valuat_1 @ C @ A @ B ) => ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ ( k6_qc_lang1 @ A ) @ ( k3_margrel1 @ B ) ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k6_qc_lang1 @ A ) @ ( k3_margrel1 @ B ) ) ) ) ) ) ) ),file(valuat_1,m1_valuat_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_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ B ) & ( m1_funct_2 @ C @ A @ B ) ) => ! [D: $i] : ( ( m2_funct_2 @ D @ A @ B @ C ) => ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ A @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),file(funct_2,m2_funct_2)).
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_112__sublemma,axiom,( m1_qc_lang1 @ c1_112__sublemma ),file(sublemma,c1_112__sublemma)).
thf(dt_c2_112__sublemma,axiom,( ~ ( v1_xboole_0 @ c2_112__sublemma ) ),file(sublemma,c2_112__sublemma)).
thf(dt_c3_112__sublemma,axiom,( m1_valuat_1 @ c3_112__sublemma @ c1_112__sublemma @ c2_112__sublemma ),file(sublemma,c3_112__sublemma)).
thf(cc18_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_membered)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( ( v1_relat_1 @ A ) & ~ ( v1_xboole_0 @ A ) ) ) ),file(qc_lang1,cc1_qc_lang1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc25_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ( v6_membered @ A ) ) ),file(membered,cc25_membered)).
thf(cc26_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_membered @ A ) ) ),file(membered,cc26_membered)).
thf(cc2_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc2_card_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
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(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc1_substut1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k1_substut1 @ A ) ) ) ),file(substut1,fc1_substut1)).
thf(fc2_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k2_qc_lang1 @ A ) ) ) ),file(qc_lang1,fc2_qc_lang1)).
thf(fc2_substut1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( v4_funct_1 @ ( k1_substut1 @ A ) ) ) ),file(substut1,fc2_substut1)).
thf(fc3_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k3_qc_lang1 @ A ) ) ) ),file(qc_lang1,fc3_qc_lang1)).
thf(fc4_substut1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( ~ ( v1_xboole_0 @ ( k16_substut1 @ A ) ) & ( v1_substut1 @ ( k16_substut1 @ A ) @ A ) ) ) ),file(substut1,fc4_substut1)).
thf(fc6_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k6_qc_lang1 @ A ) ) ) ),file(qc_lang1,fc6_qc_lang1)).
thf(fc7_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k5_numbers ) & ( m1_qc_lang1 @ B ) ) => ~ ( v1_xboole_0 @ ( k8_qc_lang1 @ B @ A ) ) ) ),file(qc_lang1,fc7_qc_lang1)).
thf(fc7_substut1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k38_substut1 @ A ) ) ) ),file(substut1,fc7_substut1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(e1_112__sublemma,axiom,( ! [A: $i] : ( ( m2_subset_1 @ A @ ( k16_substut1 @ c1_112__sublemma ) @ ( k38_substut1 @ c1_112__sublemma ) ) => ! [B: $i] : ( ( m2_subset_1 @ B @ ( k16_substut1 @ c1_112__sublemma ) @ ( k38_substut1 @ c1_112__sublemma ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ ( k2_qc_lang1 @ c1_112__sublemma ) @ ( k3_qc_lang1 @ c1_112__sublemma ) ) => ! [D: $i] : ( ( m1_substut1 @ D @ c1_112__sublemma @ ( k7_sublemma @ c1_112__sublemma @ A @ C ) ) => ! [E: $i] : ( ( m1_subset_1 @ E @ k5_numbers ) => ! [F: $i] : ( ( ( v5_relat_1 @ F @ ( k3_qc_lang1 @ c1_112__sublemma ) ) & ( v3_card_1 @ F @ E ) & ( m2_finseq_1 @ F @ ( k2_qc_lang1 @ c1_112__sublemma ) ) ) => ! [G: $i] : ( ( m2_subset_1 @ G @ ( k6_qc_lang1 @ c1_112__sublemma ) @ ( k8_qc_lang1 @ c1_112__sublemma @ E ) ) => ! [H: $i] : ( ( m1_subset_1 @ H @ ( k1_substut1 @ c1_112__sublemma ) ) => ( ! [I: $i] : ( ( m2_funct_2 @ I @ ( k3_qc_lang1 @ c1_112__sublemma ) @ c2_112__sublemma @ ( k2_valuat_1 @ c1_112__sublemma @ c2_112__sublemma ) ) => ( ( r1_valuat_1 @ c1_112__sublemma @ c2_112__sublemma @ ( k39_substut1 @ c1_112__sublemma @ ( k4_sublemma @ E @ c1_112__sublemma @ G @ F @ H ) ) @ c3_112__sublemma @ I ) <=> ( r1_sublemma @ c1_112__sublemma @ ( k4_sublemma @ E @ c1_112__sublemma @ G @ F @ H ) @ c2_112__sublemma @ ( k1_sublemma @ c1_112__sublemma @ c2_112__sublemma @ I @ ( k3_sublemma @ c1_112__sublemma @ ( k4_sublemma @ E @ c1_112__sublemma @ G @ F @ H ) @ c2_112__sublemma @ I ) ) @ c3_112__sublemma ) ) ) & ( ( v2_substut1 @ A @ c1_112__sublemma ) => ! [I: $i] : ( ( m2_funct_2 @ I @ ( k3_qc_lang1 @ c1_112__sublemma ) @ c2_112__sublemma @ ( k2_valuat_1 @ c1_112__sublemma @ c2_112__sublemma ) ) => ( ( r1_valuat_1 @ c1_112__sublemma @ c2_112__sublemma @ ( k39_substut1 @ c1_112__sublemma @ A ) @ c3_112__sublemma @ I ) <=> ( r1_sublemma @ c1_112__sublemma @ A @ c2_112__sublemma @ ( k1_sublemma @ c1_112__sublemma @ c2_112__sublemma @ I @ ( k3_sublemma @ c1_112__sublemma @ A @ c2_112__sublemma @ I ) ) @ c3_112__sublemma ) ) ) ) & ( ! [I: $i] : ( ( m2_funct_2 @ I @ ( k3_qc_lang1 @ c1_112__sublemma ) @ c2_112__sublemma @ ( k2_valuat_1 @ c1_112__sublemma @ c2_112__sublemma ) ) => ( ( r1_valuat_1 @ c1_112__sublemma @ c2_112__sublemma @ ( k39_substut1 @ c1_112__sublemma @ A ) @ c3_112__sublemma @ I ) <=> ( r1_sublemma @ c1_112__sublemma @ A @ c2_112__sublemma @ ( k1_sublemma @ c1_112__sublemma @ c2_112__sublemma @ I @ ( k3_sublemma @ c1_112__sublemma @ A @ c2_112__sublemma @ I ) ) @ c3_112__sublemma ) ) ) => ! [I: $i] : ( ( m2_funct_2 @ I @ ( k3_qc_lang1 @ c1_112__sublemma ) @ c2_112__sublemma @ ( k2_valuat_1 @ c1_112__sublemma @ c2_112__sublemma ) ) => ( ( r1_valuat_1 @ c1_112__sublemma @ c2_112__sublemma @ ( k39_substut1 @ c1_112__sublemma @ ( k5_sublemma @ c1_112__sublemma @ A ) ) @ c3_112__sublemma @ I ) <=> ( r1_sublemma @ c1_112__sublemma @ ( k5_sublemma @ c1_112__sublemma @ A ) @ c2_112__sublemma @ ( k1_sublemma @ c1_112__sublemma @ c2_112__sublemma @ I @ ( k3_sublemma @ c1_112__sublemma @ ( k5_sublemma @ c1_112__sublemma @ A ) @ c2_112__sublemma @ I ) ) @ c3_112__sublemma ) ) ) ) & ( ( ( = @ ( k19_substut1 @ c1_112__sublemma @ A ) @ ( k19_substut1 @ c1_112__sublemma @ B ) ) & ! [I: $i] : ( ( m2_funct_2 @ I @ ( k3_qc_lang1 @ c1_112__sublemma ) @ c2_112__sublemma @ ( k2_valuat_1 @ c1_112__sublemma @ c2_112__sublemma ) ) => ( ( r1_valuat_1 @ c1_112__sublemma @ c2_112__sublemma @ ( k39_substut1 @ c1_112__sublemma @ A ) @ c3_112__sublemma @ I ) <=> ( r1_sublemma @ c1_112__sublemma @ A @ c2_112__sublemma @ ( k1_sublemma @ c1_112__sublemma @ c2_112__sublemma @ I @ ( k3_sublemma @ c1_112__sublemma @ A @ c2_112__sublemma @ I ) ) @ c3_112__sublemma ) ) ) & ! [I: $i] : ( ( m2_funct_2 @ I @ ( k3_qc_lang1 @ c1_112__sublemma ) @ c2_112__sublemma @ ( k2_valuat_1 @ c1_112__sublemma @ c2_112__sublemma ) ) => ( ( r1_valuat_1 @ c1_112__sublemma @ c2_112__sublemma @ ( k39_substut1 @ c1_112__sublemma @ B ) @ c3_112__sublemma @ I ) <=> ( r1_sublemma @ c1_112__sublemma @ B @ c2_112__sublemma @ ( k1_sublemma @ c1_112__sublemma @ c2_112__sublemma @ I @ ( k3_sublemma @ c1_112__sublemma @ B @ c2_112__sublemma @ I ) ) @ c3_112__sublemma ) ) ) ) => ! [I: $i] : ( ( m2_funct_2 @ I @ ( k3_qc_lang1 @ c1_112__sublemma ) @ c2_112__sublemma @ ( k2_valuat_1 @ c1_112__sublemma @ c2_112__sublemma ) ) => ( ( r1_valuat_1 @ c1_112__sublemma @ c2_112__sublemma @ ( k39_substut1 @ c1_112__sublemma @ ( k6_sublemma @ c1_112__sublemma @ A @ B ) ) @ c3_112__sublemma @ I ) <=> ( r1_sublemma @ c1_112__sublemma @ ( k6_sublemma @ c1_112__sublemma @ A @ B ) @ c2_112__sublemma @ ( k1_sublemma @ c1_112__sublemma @ c2_112__sublemma @ I @ ( k3_sublemma @ c1_112__sublemma @ ( k6_sublemma @ c1_112__sublemma @ A @ B ) @ c2_112__sublemma @ I ) ) @ c3_112__sublemma ) ) ) ) & ( ( ( v3_substut1 @ ( k7_sublemma @ c1_112__sublemma @ A @ C ) @ c1_112__sublemma ) & ! [I: $i] : ( ( m2_funct_2 @ I @ ( k3_qc_lang1 @ c1_112__sublemma ) @ c2_112__sublemma @ ( k2_valuat_1 @ c1_112__sublemma @ c2_112__sublemma ) ) => ( ( r1_valuat_1 @ c1_112__sublemma @ c2_112__sublemma @ ( k39_substut1 @ c1_112__sublemma @ A ) @ c3_112__sublemma @ I ) <=> ( r1_sublemma @ c1_112__sublemma @ A @ c2_112__sublemma @ ( k1_sublemma @ c1_112__sublemma @ c2_112__sublemma @ I @ ( k3_sublemma @ c1_112__sublemma @ A @ c2_112__sublemma @ I ) ) @ c3_112__sublemma ) ) ) ) => ! [I: $i] : ( ( m2_funct_2 @ I @ ( k3_qc_lang1 @ c1_112__sublemma ) @ c2_112__sublemma @ ( k2_valuat_1 @ c1_112__sublemma @ c2_112__sublemma ) ) => ( ( r1_valuat_1 @ c1_112__sublemma @ c2_112__sublemma @ ( k39_substut1 @ c1_112__sublemma @ ( k9_sublemma @ c1_112__sublemma @ ( k7_sublemma @ c1_112__sublemma @ A @ C ) @ D ) ) @ c3_112__sublemma @ I ) <=> ( r1_sublemma @ c1_112__sublemma @ ( k9_sublemma @ c1_112__sublemma @ ( k7_sublemma @ c1_112__sublemma @ A @ C ) @ D ) @ c2_112__sublemma @ ( k1_sublemma @ c1_112__sublemma @ c2_112__sublemma @ I @ ( k3_sublemma @ c1_112__sublemma @ ( k9_sublemma @ c1_112__sublemma @ ( k7_sublemma @ c1_112__sublemma @ A @ C ) @ D ) @ c2_112__sublemma @ I ) ) @ c3_112__sublemma ) ) ) ) ) ) ) ) ) ) ) ) ) ),file(sublemma,e1_112__sublemma)).
thf(s1_sublemma,axiom,( ! [A: $i > $o] : ! [B: $i] : ( ( m1_qc_lang1 @ B ) => ( ! [C: $i] : ( ( m2_subset_1 @ C @ ( k16_substut1 @ B ) @ ( k38_substut1 @ B ) ) => ! [D: $i] : ( ( m2_subset_1 @ D @ ( k16_substut1 @ B ) @ ( k38_substut1 @ B ) ) => ! [E: $i] : ( ( m2_subset_1 @ E @ ( k2_qc_lang1 @ B ) @ ( k3_qc_lang1 @ B ) ) => ! [F: $i] : ( ( m1_substut1 @ F @ B @ ( k7_sublemma @ B @ C @ E ) ) => ! [G: $i] : ( ( m1_subset_1 @ G @ k5_numbers ) => ! [H: $i] : ( ( ( v5_relat_1 @ H @ ( k3_qc_lang1 @ B ) ) & ( v3_card_1 @ H @ G ) & ( m2_finseq_1 @ H @ ( k2_qc_lang1 @ B ) ) ) => ! [I: $i] : ( ( m2_subset_1 @ I @ ( k6_qc_lang1 @ B ) @ ( k8_qc_lang1 @ B @ G ) ) => ! [J: $i] : ( ( m1_subset_1 @ J @ ( k1_substut1 @ B ) ) => ( ( A @ ( k4_sublemma @ G @ B @ I @ H @ J ) ) & ( ( v2_substut1 @ C @ B ) => ( A @ C ) ) & ( ( A @ C ) => ( A @ ( k5_sublemma @ B @ C ) ) ) & ( ( ( = @ ( k19_substut1 @ B @ C ) @ ( k19_substut1 @ B @ D ) ) & ( A @ C ) & ( A @ D ) ) => ( A @ ( k6_sublemma @ B @ C @ D ) ) ) & ( ( ( v3_substut1 @ ( k7_sublemma @ B @ C @ E ) @ B ) & ( A @ C ) ) => ( A @ ( k9_sublemma @ B @ ( k7_sublemma @ B @ C @ E ) @ F ) ) ) ) ) ) ) ) ) ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ ( k16_substut1 @ B ) @ ( k38_substut1 @ B ) ) => ( A @ C ) ) ) ) ),file(sublemma,s1_sublemma)).
thf(e2_112__sublemma,conjecture,( ! [A: $i] : ( ( m2_subset_1 @ A @ ( k16_substut1 @ c1_112__sublemma ) @ ( k38_substut1 @ c1_112__sublemma ) ) => ! [B: $i] : ( ( m2_funct_2 @ B @ ( k3_qc_lang1 @ c1_112__sublemma ) @ c2_112__sublemma @ ( k2_valuat_1 @ c1_112__sublemma @ c2_112__sublemma ) ) => ( ( r1_valuat_1 @ c1_112__sublemma @ c2_112__sublemma @ ( k39_substut1 @ c1_112__sublemma @ A ) @ c3_112__sublemma @ B ) <=> ( r1_sublemma @ c1_112__sublemma @ A @ c2_112__sublemma @ ( k1_sublemma @ c1_112__sublemma @ c2_112__sublemma @ B @ ( k3_sublemma @ c1_112__sublemma @ A @ c2_112__sublemma @ B ) ) @ c3_112__sublemma ) ) ) ) ),file(sublemma,e2_112__sublemma)).
