% Mizar problem: e10_71,cqc_the3,1309,28 
include('Axioms/SET010^0.ax').
thf(c1_71_type,type,( c1_71__cqc_the3: $i )).
thf(c2_71_type,type,( c2_71__cqc_the3: $i )).
thf(k10_qc_lang1_type,type,( k10_qc_lang1: $i > $i > $i > $i )).
thf(k12_qc_lang1_type,type,( k12_qc_lang1: $i > $i )).
thf(k13_cqc_lang_type,type,( k13_cqc_lang: $i > $i > $i > $i )).
thf(k13_qc_lang1_type,type,( k13_qc_lang1: $i > $i > $i )).
thf(k14_qc_lang1_type,type,( k14_qc_lang1: $i > $i > $i > $i )).
thf(k15_qc_lang1_type,type,( k15_qc_lang1: $i > $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_tarski_type,type,( k1_tarski: $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k24_qc_lang1_type,type,( k24_qc_lang1: $i > $i > $i )).
thf(k2_qc_lang1_type,type,( k2_qc_lang1: $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_cqc_lang_type,type,( k3_cqc_lang: $i > $i )).
thf(k3_qc_lang1_type,type,( k3_qc_lang1: $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_cqc_lang_type,type,( k5_cqc_lang: $i > $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k6_qc_lang1_type,type,( k6_qc_lang1: $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(m1_finseq_1_type,type,( m1_finseq_1: $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(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_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v1_finseq_1_type,type,( v1_finseq_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_int_1_type,type,( v1_int_1: $i > $o )).
thf(v1_membered_type,type,( v1_membered: $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_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(v2_membered_type,type,( v2_membered: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v3_card_1_type,type,( v3_card_1: $i > $i > $o )).
thf(v3_membered_type,type,( v3_membered: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_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(v5_membered_type,type,( v5_membered: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v6_membered_type,type,( v6_membered: $i > $o )).
thf(v7_membered_type,type,( v7_membered: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(fc10_membered,axiom,( ! [A: $i] : ( ( v1_rat_1 @ A ) => ( v4_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc10_membered)).
thf(fc7_membered,axiom,( ! [A: $i] : ( ( v1_xcmplx_0 @ A ) => ( v1_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc7_membered)).
thf(fc8_membered,axiom,( ! [A: $i] : ( ( v1_xxreal_0 @ A ) => ( v2_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc8_membered)).
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(cc13_membered,axiom,( ! [A: $i] : ( ( v2_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xxreal_0 @ B ) ) ) ),file(membered,cc13_membered)).
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(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(cc3_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
thf(fc11_membered,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v5_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc11_membered)).
thf(fc25_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_membered @ A ) & ( v1_membered @ B ) ) => ( v1_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),file(membered,fc25_membered)).
thf(fc26_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v2_membered @ A ) & ( v2_membered @ B ) ) => ( v2_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),file(membered,fc26_membered)).
thf(fc28_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v4_membered @ A ) & ( v4_membered @ B ) ) => ( v4_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),file(membered,fc28_membered)).
thf(fc9_membered,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v3_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc9_membered)).
thf(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
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_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ( v4_membered @ A ) ) ),file(membered,cc2_membered)).
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_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(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(cc4_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
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(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_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_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_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(fc12_membered,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v6_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc12_membered)).
thf(fc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) ) => ( v4_relat_1 @ ( k2_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc1_relset_1)).
thf(fc27_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_membered @ A ) & ( v3_membered @ B ) ) => ( v3_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),file(membered,fc27_membered)).
thf(fc29_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_membered @ A ) & ( v5_membered @ B ) ) => ( v5_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),file(membered,fc29_membered)).
thf(fc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) ) => ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(relat_1,fc3_relat_1)).
thf(fc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) ) => ( v5_relat_1 @ ( k2_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc4_relset_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_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(rc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relset_1,rc1_relset_1)).
thf(rc3_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) & ( v7_membered @ A ) ) ),file(membered,rc3_membered)).
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_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(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_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_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(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(cc18_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_membered @ A ) ) ),file(membered,cc18_membered)).
thf(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
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(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(cc26_membered,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_membered @ A ) ) ),file(membered,cc26_membered)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc3_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( ( v1_xboole_0 @ B ) => ( v1_subset_1 @ B @ A ) ) ) ) ),file(subset_1,cc3_subset_1)).
thf(cc4_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc4_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ~ ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,cc4_subset_1)).
thf(cc8_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) ) => ( v3_membered @ A ) ) ),file(membered,cc8_membered)).
thf(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc2_cqc_lang,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ~ ( v1_xboole_0 @ ( k3_cqc_lang @ A ) ) ) ),file(cqc_lang,fc2_cqc_lang)).
thf(fc30_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v6_membered @ A ) & ( v6_membered @ B ) ) => ( v6_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),file(membered,fc30_membered)).
thf(fc3_membered,axiom,( v3_membered @ k1_numbers ),file(membered,fc3_membered)).
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(fc6_membered,axiom,( v6_membered @ k4_ordinal1 ),file(membered,fc6_membered)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(rc1_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc1_membered)).
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(commutativity_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ A ) ) ),file(xboole_0,k2_xboole_0)).
thf(idempotence_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k2_xboole_0)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(redefinition_k5_cqc_lang,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( = @ ( k5_cqc_lang @ A ) @ ( k12_qc_lang1 @ A ) ) ) ),file(cqc_lang,k5_cqc_lang)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
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(dt_k10_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k6_qc_lang1 @ A ) ) & ( m1_finseq_1 @ C @ ( k2_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k10_qc_lang1 @ A @ B @ C ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k10_qc_lang1)).
thf(dt_k12_qc_lang1,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( m1_subset_1 @ ( k12_qc_lang1 @ A ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k12_qc_lang1)).
thf(dt_k13_cqc_lang,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) & ( m1_subset_1 @ C @ ( k3_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k13_cqc_lang @ A @ B @ C ) @ ( k9_qc_lang1 @ A ) ) ) ),file(cqc_lang,k13_cqc_lang)).
thf(dt_k13_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k13_qc_lang1 @ A @ B ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k13_qc_lang1)).
thf(dt_k14_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) & ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k14_qc_lang1 @ A @ B @ C ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k14_qc_lang1)).
thf(dt_k15_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k3_qc_lang1 @ A ) ) & ( m1_subset_1 @ C @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k15_qc_lang1 @ A @ B @ C ) @ ( k9_qc_lang1 @ A ) ) ) ),file(qc_lang1,k15_qc_lang1)).
thf(dt_k1_tarski,axiom,( $true ),file(tarski,k1_tarski)).
thf(dt_k24_qc_lang1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_qc_lang1 @ A ) & ( m1_subset_1 @ B @ ( k9_qc_lang1 @ A ) ) ) => ( m1_subset_1 @ ( k24_qc_lang1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k3_qc_lang1 @ A ) ) ) ) ),file(qc_lang1,k24_qc_lang1)).
thf(dt_k2_qc_lang1,axiom,( $true ),file(qc_lang1,k2_qc_lang1)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
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_k5_cqc_lang,axiom,( ! [A: $i] : ( ( m1_qc_lang1 @ A ) => ( m2_subset_1 @ ( k5_cqc_lang @ A ) @ ( k9_qc_lang1 @ A ) @ ( k3_cqc_lang @ A ) ) ) ),file(cqc_lang,k5_cqc_lang)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k6_qc_lang1,axiom,( $true ),file(qc_lang1,k6_qc_lang1)).
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_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_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_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_71__cqc_the3,axiom,( m1_qc_lang1 @ c1_71__cqc_the3 ),file(cqc_the3,c1_71__cqc_the3)).
thf(dt_c2_71__cqc_the3,axiom,( m2_subset_1 @ c2_71__cqc_the3 @ ( k2_qc_lang1 @ c1_71__cqc_the3 ) @ ( k3_qc_lang1 @ c1_71__cqc_the3 ) ),file(cqc_the3,c2_71__cqc_the3)).
thf(cc25_membered,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ( v6_membered @ A ) ) ),file(membered,cc25_membered)).
thf(e4_71__cqc_the3,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k5_numbers ) => ! [B: $i] : ( ( m2_subset_1 @ B @ ( k6_qc_lang1 @ c1_71__cqc_the3 ) @ ( k8_qc_lang1 @ c1_71__cqc_the3 @ A ) ) => ! [C: $i] : ( ( ( v3_card_1 @ C @ A ) & ( m2_finseq_1 @ C @ ( k2_qc_lang1 @ c1_71__cqc_the3 ) ) ) => ( r1_tarski @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_cqc_lang @ c1_71__cqc_the3 @ ( k10_qc_lang1 @ c1_71__cqc_the3 @ B @ C ) @ c2_71__cqc_the3 ) ) @ ( k2_xboole_0 @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k10_qc_lang1 @ c1_71__cqc_the3 @ B @ C ) ) @ ( k1_tarski @ c2_71__cqc_the3 ) ) ) ) ) ) ),file(cqc_the3,e4_71__cqc_the3)).
thf(e9_71__cqc_the3,axiom,( r1_tarski @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_cqc_lang @ c1_71__cqc_the3 @ ( k5_cqc_lang @ c1_71__cqc_the3 ) @ c2_71__cqc_the3 ) ) @ ( k2_xboole_0 @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k5_cqc_lang @ c1_71__cqc_the3 ) ) @ ( k1_tarski @ c2_71__cqc_the3 ) ) ),file(cqc_the3,e9_71__cqc_the3)).
thf(e1_71__cqc_the3,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k9_qc_lang1 @ c1_71__cqc_the3 ) ) => ( ( r1_tarski @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_cqc_lang @ c1_71__cqc_the3 @ A @ c2_71__cqc_the3 ) ) @ ( k2_xboole_0 @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ A ) @ ( k1_tarski @ c2_71__cqc_the3 ) ) ) => ( r1_tarski @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_cqc_lang @ c1_71__cqc_the3 @ ( k13_qc_lang1 @ c1_71__cqc_the3 @ A ) @ c2_71__cqc_the3 ) ) @ ( k2_xboole_0 @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_qc_lang1 @ c1_71__cqc_the3 @ A ) ) @ ( k1_tarski @ c2_71__cqc_the3 ) ) ) ) ) ),file(cqc_the3,e1_71__cqc_the3)).
thf(e2_71__cqc_the3,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k9_qc_lang1 @ c1_71__cqc_the3 ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ c1_71__cqc_the3 ) ) => ( ( ( r1_tarski @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_cqc_lang @ c1_71__cqc_the3 @ A @ c2_71__cqc_the3 ) ) @ ( k2_xboole_0 @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ A ) @ ( k1_tarski @ c2_71__cqc_the3 ) ) ) & ( r1_tarski @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_cqc_lang @ c1_71__cqc_the3 @ B @ c2_71__cqc_the3 ) ) @ ( k2_xboole_0 @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ B ) @ ( k1_tarski @ c2_71__cqc_the3 ) ) ) ) => ( r1_tarski @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_cqc_lang @ c1_71__cqc_the3 @ ( k14_qc_lang1 @ c1_71__cqc_the3 @ A @ B ) @ c2_71__cqc_the3 ) ) @ ( k2_xboole_0 @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k14_qc_lang1 @ c1_71__cqc_the3 @ A @ B ) ) @ ( k1_tarski @ c2_71__cqc_the3 ) ) ) ) ) ) ),file(cqc_the3,e2_71__cqc_the3)).
thf(e3_71__cqc_the3,axiom,( ! [A: $i] : ( ( m2_subset_1 @ A @ ( k2_qc_lang1 @ c1_71__cqc_the3 ) @ ( k3_qc_lang1 @ c1_71__cqc_the3 ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k9_qc_lang1 @ c1_71__cqc_the3 ) ) => ( ( r1_tarski @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_cqc_lang @ c1_71__cqc_the3 @ B @ c2_71__cqc_the3 ) ) @ ( k2_xboole_0 @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ B ) @ ( k1_tarski @ c2_71__cqc_the3 ) ) ) => ( r1_tarski @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_cqc_lang @ c1_71__cqc_the3 @ ( k15_qc_lang1 @ c1_71__cqc_the3 @ A @ B ) @ c2_71__cqc_the3 ) ) @ ( k2_xboole_0 @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k15_qc_lang1 @ c1_71__cqc_the3 @ A @ B ) ) @ ( k1_tarski @ c2_71__cqc_the3 ) ) ) ) ) ) ),file(cqc_the3,e3_71__cqc_the3)).
thf(s1_qc_lang1,axiom,( ! [A: $i > $o] : ! [B: $i] : ( ( ! [C: $i] : ( ( m1_subset_1 @ C @ k5_numbers ) => ! [D: $i] : ( ( m2_subset_1 @ D @ ( k6_qc_lang1 @ B ) @ ( k8_qc_lang1 @ B @ C ) ) => ! [E: $i] : ( ( ( v3_card_1 @ E @ C ) & ( m2_finseq_1 @ E @ ( k2_qc_lang1 @ B ) ) ) => ( A @ ( k10_qc_lang1 @ B @ D @ E ) ) ) ) ) & ( A @ ( k12_qc_lang1 @ B ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ B ) ) => ( ( A @ C ) => ( A @ ( k13_qc_lang1 @ B @ C ) ) ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ B ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k9_qc_lang1 @ B ) ) => ( ( ( A @ C ) & ( A @ D ) ) => ( A @ ( k14_qc_lang1 @ B @ C @ D ) ) ) ) ) & ! [C: $i] : ( ( m2_subset_1 @ C @ ( k2_qc_lang1 @ B ) @ ( k3_qc_lang1 @ B ) ) => ! [D: $i] : ( ( m1_subset_1 @ D @ ( k9_qc_lang1 @ B ) ) => ( ( A @ D ) => ( A @ ( k15_qc_lang1 @ B @ C @ D ) ) ) ) ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k9_qc_lang1 @ B ) ) => ( A @ C ) ) ) ),file(qc_lang1,s1_qc_lang1)).
thf(e10_71__cqc_the3,conjecture,( ! [A: $i] : ( ( m1_subset_1 @ A @ ( k9_qc_lang1 @ c1_71__cqc_the3 ) ) => ( r1_tarski @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ ( k13_cqc_lang @ c1_71__cqc_the3 @ A @ c2_71__cqc_the3 ) ) @ ( k2_xboole_0 @ ( k24_qc_lang1 @ c1_71__cqc_the3 @ A ) @ ( k1_tarski @ c2_71__cqc_the3 ) ) ) ) ),file(cqc_the3,e10_71__cqc_the3)).
