% Mizar problem: s1_pcomps_2,pcomps_2,127,8 
include('Axioms/SET010^0.ax').
thf(f1_s1_pcomps_2_type,type,( f1_s1_pcomps_2: $i )).
thf(f2_s1_pcomps_2_type,type,( f2_s1_pcomps_2: $i )).
thf(k1_tarski_type,type,( k1_tarski: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_tarski_type,type,( k2_tarski: $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(p1_s1_pcomps_2_type,type,( p1_s1_pcomps_2: $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r2_wellord1_type,type,( r2_wellord1: $i > $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_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_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_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_membered_type,type,( v2_membered: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_finseq_1_type,type,( v3_finseq_1: $i > $o )).
thf(v3_membered_type,type,( v3_membered: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_xxreal_0_type,type,( v3_xxreal_0: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_membered_type,type,( v4_membered: $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_membered_type,type,( v5_membered: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v6_membered_type,type,( v6_membered: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_membered_type,type,( v7_membered: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(cc10_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finseq_1 @ B ) ) ) ),file(finseq_1,cc10_finseq_1)).
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_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_finseq_1 @ B ) ) ) ),file(finseq_1,cc11_finseq_1)).
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(cc14_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_xreal_0 @ B ) ) ) ),file(membered,cc14_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(cc16_membered,axiom,( ! [A: $i] : ( ( v5_membered @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_int_1 @ B ) ) ) ),file(membered,cc16_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(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(cc1_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc1_finseq_1)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_membered,axiom,( ! [A: $i] : ( ( v6_membered @ A ) => ( v5_membered @ A ) ) ),file(membered,cc1_membered)).
thf(cc1_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) ) ),file(nat_1,cc1_nat_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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(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(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(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(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(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_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc2_finset_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(cc2_xxreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,cc2_xxreal_0)).
thf(cc3_membered,axiom,( ! [A: $i] : ( ( v4_membered @ A ) => ( v3_membered @ A ) ) ),file(membered,cc3_membered)).
thf(cc3_nat_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v3_xxreal_0 @ A ) ) ) ),file(nat_1,cc3_nat_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
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_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_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc4_finseq_1)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc4_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v2_membered @ A ) ) ),file(membered,cc4_membered)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
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(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(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(cc5_membered,axiom,( ! [A: $i] : ( ( v3_membered @ A ) => ( v1_membered @ A ) ) ),file(membered,cc5_membered)).
thf(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
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(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
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(cc7_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc7_finset_1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
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(cc8_finseq_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_finseq_1 @ A ) ) ),file(finseq_1,cc8_finseq_1)).
thf(cc8_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v5_finset_1 @ B ) ) ) ),file(finset_1,cc8_finset_1)).
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(cc9_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ( v4_funct_1 @ A ) ) ),file(finseq_1,cc9_finseq_1)).
thf(cc9_finset_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_finset_1 @ A ) ) ) ),file(finset_1,cc9_finset_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(commutativity_k2_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ B @ A ) ) ),file(tarski,k2_tarski)).
thf(d2_xboole_0,axiom,( = @ k1_xboole_0 @ ( eps @ ^ [A: $i] : ( v1_xboole_0 @ A ) ) ),file(xboole_0,d2_xboole_0)).
thf(d3_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( ( r1_tarski @ A @ B ) <=> ! [C: $i] : ( ( r2_hidden @ C @ A ) => ( r2_hidden @ C @ B ) ) ) ),file(tarski,d3_tarski)).
thf(d5_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k4_tarski @ A @ B ) @ ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ) ),file(tarski,d5_tarski)).
thf(dt_f1_s1_pcomps_2,axiom,( $true ),file(pcomps_2,f1_s1_pcomps_2)).
thf(dt_f2_s1_pcomps_2,axiom,( v1_relat_1 @ f2_s1_pcomps_2 ),file(pcomps_2,f2_s1_pcomps_2)).
thf(dt_k1_tarski,axiom,( $true ),file(tarski,k1_tarski)).
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_k2_tarski,axiom,( $true ),file(tarski,k2_tarski)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(fc10_membered,axiom,( ! [A: $i] : ( ( v1_rat_1 @ A ) => ( v4_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc10_membered)).
thf(fc11_membered,axiom,( ! [A: $i] : ( ( v1_int_1 @ A ) => ( v5_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc11_membered)).
thf(fc12_membered,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v6_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc12_membered)).
thf(fc13_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xcmplx_0 @ A ) & ( v1_xcmplx_0 @ B ) ) => ( v1_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc13_membered)).
thf(fc14_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xxreal_0 @ A ) & ( v1_xxreal_0 @ B ) ) => ( v2_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc14_membered)).
thf(fc15_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xreal_0 @ A ) & ( v1_xreal_0 @ B ) ) => ( v3_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc15_membered)).
thf(fc16_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_rat_1 @ A ) & ( v1_rat_1 @ B ) ) => ( v4_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc16_membered)).
thf(fc17_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc17_finset_1)).
thf(fc17_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_int_1 @ A ) & ( v1_int_1 @ B ) ) => ( v5_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc17_membered)).
thf(fc18_membered,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v7_ordinal1 @ A ) & ( v7_ordinal1 @ B ) ) => ( v6_membered @ ( k2_tarski @ A @ B ) ) ) ),file(membered,fc18_membered)).
thf(fc1_finset_1,axiom,( ! [A: $i] : ( v1_finset_1 @ ( k1_tarski @ A ) ) ),file(finset_1,fc1_finset_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc2_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),file(finset_1,fc2_finset_1)).
thf(fc30_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_tarski @ A ) ) ) ),file(finset_1,fc30_finset_1)).
thf(fc31_finset_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v5_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(finset_1,fc31_finset_1)).
thf(fc32_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v5_finset_1 @ ( k2_tarski @ A @ B ) ) ) ),file(finset_1,fc32_finset_1)).
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(fc9_membered,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v3_membered @ ( k1_tarski @ A ) ) ) ),file(membered,fc9_membered)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_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_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_xxreal_0,axiom,( ? [A: $i] : ( v1_xxreal_0 @ A ) ),file(xxreal_0,rc1_xxreal_0)).
thf(rc2_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_xboole_0 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc2_finset_1)).
thf(rc2_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) ) ),file(membered,rc2_membered)).
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_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_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v2_xxreal_0 @ A ) ) ),file(xxreal_0,rc2_xxreal_0)).
thf(rc3_membered,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v6_membered @ A ) & ( v7_membered @ A ) ) ),file(membered,rc3_membered)).
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(rc3_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xxreal_0 @ A ) & ( v3_xxreal_0 @ A ) ) ),file(xxreal_0,rc3_xxreal_0)).
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(rc4_xxreal_0,axiom,( ? [A: $i] : ( ( v1_xboole_0 @ A ) & ( v1_xxreal_0 @ A ) ) ),file(xxreal_0,rc4_xxreal_0)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
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_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(rc7_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_zfmisc_1 @ B ) & ( v1_finset_1 @ B ) ) ) ),file(finset_1,rc7_finset_1)).
thf(rc8_finseq_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v3_finseq_1 @ A ) ) ),file(finseq_1,rc8_finseq_1)).
thf(rc8_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t2_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ B ) => ( ( v1_xboole_0 @ B ) | ( r2_hidden @ A @ B ) ) ) ),file(subset,t2_subset)).
thf(t3_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) <=> ( r1_tarski @ A @ B ) ) ),file(subset,t3_subset)).
thf(t4_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) ) => ( m1_subset_1 @ A @ C ) ) ),file(subset,t4_subset)).
thf(t5_subset,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ~ ( ( r2_hidden @ A @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) & ( v1_xboole_0 @ C ) ) ),file(subset,t5_subset)).
thf(t5_wellord1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ B ) => ( ( r2_wellord1 @ B @ A ) => ! [C: $i] : ~ ( ( r1_tarski @ C @ A ) & ~ ( = @ C @ k1_xboole_0 ) & ! [D: $i] : ~ ( ( r2_hidden @ D @ C ) & ! [E: $i] : ( ( r2_hidden @ E @ C ) => ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) ) ) ) ) ),file(wellord1,t5_wellord1)).
thf(t6_boole,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( = @ A @ k1_xboole_0 ) ) ),file(boole,t6_boole)).
thf(t7_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t7_boole)).
thf(t8_boole,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( v1_xboole_0 @ A ) & ~ ( = @ A @ B ) & ( v1_xboole_0 @ B ) ) ),file(boole,t8_boole)).
thf(s1_xboole_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ? [C: $i] : ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( r2_hidden @ D @ B ) & ( A @ D ) ) ) ),file(xboole_0,s1_xboole_0)).
thf(s1_pcomps_2,conjecture,( ( ( r2_wellord1 @ f2_s1_pcomps_2 @ f1_s1_pcomps_2 ) & ? [A: $i] : ( ( r2_hidden @ A @ f1_s1_pcomps_2 ) & ( p1_s1_pcomps_2 @ A ) ) ) => ? [A: $i] : ( ( r2_hidden @ A @ f1_s1_pcomps_2 ) & ( p1_s1_pcomps_2 @ A ) & ! [B: $i] : ( ( ( r2_hidden @ B @ f1_s1_pcomps_2 ) & ( p1_s1_pcomps_2 @ B ) ) => ( r2_hidden @ ( k4_tarski @ A @ B ) @ f2_s1_pcomps_2 ) ) ) ),file(pcomps_2,s1_pcomps_2)).
