% Mizar problem: s25_fraenkel,fraenkel,795,7 
include('Axioms/SET010^1.ax').
thf(f1_s25_fraenkel_type,type,( f1_s25_fraenkel: $i )).
thf(f2_s25_fraenkel_type,type,( f2_s25_fraenkel: $i )).
thf(f3_s25_fraenkel_type,type,( f3_s25_fraenkel: $i )).
thf(f4_s25_fraenkel_type,type,( f4_s25_fraenkel: $i )).
thf(f5_s25_fraenkel_type,type,( f5_s25_fraenkel: $i > $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_funct_2_type,type,( k1_funct_2: $i > $i > $i )).
thf(k1_relset_1_type,type,( k1_relset_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(k2_partfun1_type,type,( k2_partfun1: $i > $i > $i > $i > $i )).
thf(k2_relset_1_type,type,( k2_relset_1: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_funct_2_type,type,( k3_funct_2: $i > $i > $i > $i > $i )).
thf(k3_xboole_0_type,type,( k3_xboole_0: $i > $i > $i )).
thf(k5_relat_1_type,type,( k5_relat_1: $i > $i > $i )).
thf(k7_relat_1_type,type,( k7_relat_1: $i > $i > $i )).
thf(k7_relset_1_type,type,( k7_relset_1: $i > $i > $i > $i > $i )).
thf(k8_subset_1_type,type,( k8_subset_1: $i > $i > $i > $i )).
thf(k9_funct_2_type,type,( k9_funct_2: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(m1_funct_2_type,type,( m1_funct_2: $i > $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_funct_2_type,type,( m2_funct_2: $i > $i > $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r1_xboole_0_type,type,( r1_xboole_0: $i > $i > $o )).
thf(r2_relset_1_type,type,( r2_relset_1: $i > $i > $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_finsub_1_type,type,( v1_finsub_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_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_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v3_finsub_1_type,type,( v3_finsub_1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v4_finsub_1_type,type,( v4_finsub_1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_1)).
thf(cc1_finsub_1,axiom,( ! [A: $i] : ( ( v4_finsub_1 @ A ) => ( ( v1_finsub_1 @ A ) & ( v3_finsub_1 @ A ) ) ) ),file(finsub_1,cc1_finsub_1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc1_subset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_xboole_0 @ B ) ) ) ),file(subset_1,cc1_subset_1)).
thf(cc2_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_finsub_1,axiom,( ! [A: $i] : ( ( ( v1_finsub_1 @ A ) & ( v3_finsub_1 @ A ) ) => ( v4_finsub_1 @ A ) ) ),file(finsub_1,cc2_finsub_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_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_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) ) => ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( v1_finset_1 @ C ) ) ) ) ) ),file(finset_1,cc3_finset_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(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_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_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(cc5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) => ( v4_relat_1 @ C @ A ) ) ) ),file(relat_1,cc5_relat_1)).
thf(cc5_subset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_zfmisc_1 @ B ) ) ) ),file(subset_1,cc5_subset_1)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_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_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_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_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_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_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(commutativity_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ A ) ) ),file(xboole_0,k3_xboole_0)).
thf(commutativity_k8_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k8_subset_1 @ A @ B @ C ) @ ( k8_subset_1 @ A @ C @ B ) ) ) ),file(subset_1,k8_subset_1)).
thf(d1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( ~ ( = @ B @ k1_xboole_0 ) => ( ( v1_funct_2 @ C @ A @ B ) <=> ( = @ A @ ( k1_relset_1 @ A @ C ) ) ) ) & ( ( = @ B @ k1_xboole_0 ) => ( ( v1_funct_2 @ C @ A @ B ) <=> ( = @ C @ k1_xboole_0 ) ) ) ) ) ),file(funct_2,d1_funct_2)).
thf(d2_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( = @ C @ ( k1_funct_2 @ A @ B ) ) <=> ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ? [E: $i] : ( ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) & ( = @ D @ E ) & ( = @ ( k9_xtuple_0 @ E ) @ A ) & ( r1_tarski @ ( k10_xtuple_0 @ E ) @ B ) ) ) ) ),file(funct_2,d2_funct_2)).
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(d6_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ! [C: $i] : ( ( = @ C @ ( k7_relat_1 @ A @ B ) ) <=> ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ? [E: $i] : ( ( r2_hidden @ E @ ( k9_xtuple_0 @ A ) ) & ( r2_hidden @ E @ B ) & ( = @ D @ ( k1_funct_1 @ A @ E ) ) ) ) ) ) ),file(funct_1,d6_funct_1)).
thf(d7_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( r1_xboole_0 @ A @ B ) <=> ( = @ ( k3_xboole_0 @ A @ B ) @ k1_xboole_0 ) ) ),file(xboole_0,d7_xboole_0)).
thf(dt_f1_s25_fraenkel,axiom,( $true ),file(fraenkel,f1_s25_fraenkel)).
thf(dt_f2_s25_fraenkel,axiom,( ~ ( v1_xboole_0 @ f2_s25_fraenkel ) ),file(fraenkel,f2_s25_fraenkel)).
thf(dt_f3_s25_fraenkel,axiom,( $true ),file(fraenkel,f3_s25_fraenkel)).
thf(dt_f4_s25_fraenkel,axiom,( $true ),file(fraenkel,f4_s25_fraenkel)).
thf(dt_f5_s25_fraenkel,axiom,( $true ),file(fraenkel,f5_s25_fraenkel)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_funct_2,axiom,( $true ),file(funct_2,k1_funct_2)).
thf(dt_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( m1_subset_1 @ ( k1_relset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(relset_1,k1_relset_1)).
thf(dt_k1_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_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) ) & ( m1_subset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),file(partfun1,k2_partfun1)).
thf(dt_k2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ( m1_subset_1 @ ( k2_relset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(relset_1,k2_relset_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ B ) ) ),file(funct_2,k3_funct_2)).
thf(dt_k3_xboole_0,axiom,( $true ),file(xboole_0,k3_xboole_0)).
thf(dt_k5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,k5_relat_1)).
thf(dt_k7_relat_1,axiom,( $true ),file(relat_1,k7_relat_1)).
thf(dt_k7_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( m1_subset_1 @ ( k7_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ) ),file(relset_1,k7_relset_1)).
thf(dt_k8_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( m1_subset_1 @ ( k8_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ),file(subset_1,k8_subset_1)).
thf(dt_k9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( m1_funct_2 @ ( k9_funct_2 @ A @ B ) @ A @ B ) ) ),file(funct_2,k9_funct_2)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_m1_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(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_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(existence_m1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( m1_funct_2 @ C @ A @ B ) ),file(funct_2,m1_funct_2)).
thf(existence_m1_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( m1_subset_1 @ B @ A ) ),file(subset_1,m1_subset_1)).
thf(existence_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 ) ) ),file(funct_2,m2_funct_2)).
thf(fc10_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ B ) => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(finset_1,fc10_finset_1)).
thf(fc10_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc10_relat_1)).
thf(fc10_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ) => ( ~ ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) ) & ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(relset_1,fc10_relset_1)).
thf(fc10_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(subset_1,fc10_subset_1)).
thf(fc11_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_finset_1 @ A ) => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(finset_1,fc11_finset_1)).
thf(fc11_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc11_relat_1)).
thf(fc11_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ) => ~ ( v1_xboole_0 @ ( k7_relat_1 @ A @ B ) ) ) ),file(relset_1,fc11_relset_1)).
thf(fc13_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v1_finset_1 @ ( k7_relat_1 @ A @ B ) ) ) ),file(finset_1,fc13_finset_1)).
thf(fc14_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),file(finset_1,fc14_finset_1)).
thf(fc16_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ B ) ) => ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) ) & ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(relat_1,fc16_relat_1)).
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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) ) & ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(relat_1,fc17_relat_1)).
thf(fc19_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_finset_1 @ A ) ) => ( v1_finset_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(finset_1,fc19_finset_1)).
thf(fc19_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ B ) ) => ( v1_xboole_0 @ ( k7_relat_1 @ A @ B ) ) ) ),file(relat_1,fc19_relat_1)).
thf(fc1_finsub_1,axiom,( ! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ) ),file(finsub_1,fc1_finsub_1)).
thf(fc1_fraenkel,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_finset_1 @ B ) ) => ( v1_finset_1 @ ( k1_funct_2 @ A @ B ) ) ) ),file(fraenkel,fc1_fraenkel)).
thf(fc1_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(relat_1,fc1_relat_1)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(fc20_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_xboole_0 @ ( k7_relat_1 @ A @ B ) ) ) ),file(relat_1,fc20_relat_1)).
thf(fc22_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_finset_1 @ A ) ) => ( v1_finset_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(finset_1,fc22_finset_1)).
thf(fc23_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v3_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(relat_1,fc23_relat_1)).
thf(fc24_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc24_relat_1)).
thf(fc25_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc25_relat_1)).
thf(fc26_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v1_finset_1 @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) & ( v1_finset_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ),file(finset_1,fc26_finset_1)).
thf(fc26_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ C @ A ) ) & ( v5_relat_1 @ ( k5_relat_1 @ C @ A ) @ B ) ) ) ),file(relat_1,fc26_relat_1)).
thf(fc27_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) & ( v1_finset_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ),file(finset_1,fc27_finset_1)).
thf(fc27_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ C @ A ) ) & ( v4_relat_1 @ ( k5_relat_1 @ C @ A ) @ A ) & ( v4_relat_1 @ ( k5_relat_1 @ C @ A ) @ B ) ) ) ),file(relat_1,fc27_relat_1)).
thf(fc2_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 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc2_relset_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(fc35_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) => ( v1_finset_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(finset_1,fc35_finset_1)).
thf(fc36_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_finset_1 @ A ) ) => ( v5_finset_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(finset_1,fc36_finset_1)).
thf(fc4_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(xtuple_0,fc4_xtuple_0)).
thf(fc5_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 @ ( k3_xboole_0 @ B @ C ) @ A ) ) ),file(relset_1,fc5_relset_1)).
thf(fc5_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(xtuple_0,fc5_xtuple_0)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(fc8_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc8_relat_1)).
thf(fc8_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) => ( v1_relat_1 @ ( k9_xtuple_0 @ D ) ) ) ),file(relset_1,fc8_relset_1)).
thf(fc9_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc9_relat_1)).
thf(fc9_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ) => ( v1_relat_1 @ ( k10_xtuple_0 @ D ) ) ) ),file(relset_1,fc9_relset_1)).
thf(idempotence_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k3_xboole_0)).
thf(idempotence_k8_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k8_subset_1 @ A @ B @ B ) @ B ) ) ),file(subset_1,k8_subset_1)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
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(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_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_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc2_subset_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_xboole_0 @ B ) ) ),file(subset_1,rc2_subset_1)).
thf(rc3_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc3_finset_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_subset_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v1_subset_1 @ B @ A ) ) ) ),file(subset_1,rc4_subset_1)).
thf(rc5_finset_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 ) & ( v1_finset_1 @ C ) ) ),file(finset_1,rc5_finset_1)).
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_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) ) => ? [C: $i] : ( ~ ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_finset_1 @ C ) ) ) ),file(finset_1,rc6_finset_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_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v5_finset_1 @ A ) ) ),file(finset_1,rc8_finset_1)).
thf(rc9_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) ),file(finset_1,rc9_finset_1)).
thf(rd4_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ( = @ ( k5_relat_1 @ A @ ( k9_xtuple_0 @ A ) ) @ A ) ) ),file(relat_1,rd4_relat_1)).
thf(rd5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( = @ ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ B ) @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,rd5_relat_1)).
thf(rd8_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( = @ ( k5_relat_1 @ B @ A ) @ B ) ) ),file(relat_1,rd8_relat_1)).
thf(redefinition_k1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) ) => ( = @ ( k1_relset_1 @ A @ B ) @ ( k9_xtuple_0 @ B ) ) ) ),file(relset_1,k1_relset_1)).
thf(redefinition_k2_partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_funct_1 @ C ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( = @ ( k2_partfun1 @ A @ B @ C @ D ) @ ( k5_relat_1 @ C @ D ) ) ) ),file(partfun1,k2_partfun1)).
thf(redefinition_k2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ( = @ ( k2_relset_1 @ A @ B ) @ ( k10_xtuple_0 @ B ) ) ) ),file(relset_1,k2_relset_1)).
thf(redefinition_k3_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ A ) ) => ( = @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_funct_1 @ C @ D ) ) ) ),file(funct_2,k3_funct_2)).
thf(redefinition_k7_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( = @ ( k7_relset_1 @ A @ B @ C @ D ) @ ( k7_relat_1 @ C @ D ) ) ) ),file(relset_1,k7_relset_1)).
thf(redefinition_k8_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( = @ ( k8_subset_1 @ A @ B @ C ) @ ( k3_xboole_0 @ B @ C ) ) ) ),file(subset_1,k8_subset_1)).
thf(redefinition_k9_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ~ ( v1_xboole_0 @ B ) => ( = @ ( k9_funct_2 @ A @ B ) @ ( k1_funct_2 @ A @ B ) ) ) ),file(funct_2,k9_funct_2)).
thf(redefinition_m2_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_r2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_relset_1 @ A @ B @ C @ D ) <=> ( = @ C @ D ) ) ) ),file(relset_1,r2_relset_1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(reflexivity_r2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( r2_relset_1 @ A @ B @ C @ C ) ) ),file(relset_1,r2_relset_1)).
thf(symmetry_r1_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( r1_xboole_0 @ A @ B ) => ( r1_xboole_0 @ B @ A ) ) ),file(xboole_0,r1_xboole_0)).
thf(symmetry_r2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( r2_relset_1 @ A @ B @ C @ D ) => ( r2_relset_1 @ A @ B @ D @ C ) ) ) ),file(relset_1,r2_relset_1)).
thf(t115_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ B ) => ( = @ ( k10_xtuple_0 @ ( k5_relat_1 @ B @ A ) ) @ ( k7_relat_1 @ B @ A ) ) ) ),file(relat_1,t115_relat_1)).
thf(t118_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ B ) => ( ( = @ ( k7_relat_1 @ B @ A ) @ k1_xboole_0 ) <=> ( r1_xboole_0 @ ( k9_xtuple_0 @ B ) @ A ) ) ) ),file(relat_1,t118_relat_1)).
thf(t17_xboole_1,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ) ),file(xboole_1,t17_xboole_1)).
thf(t19_xboole_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r1_tarski @ A @ B ) & ( r1_tarski @ A @ C ) ) => ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ) ),file(xboole_1,t19_xboole_1)).
thf(t1_subset,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ( m1_subset_1 @ A @ B ) ) ),file(subset,t1_subset)).
thf(t1_xboole_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r1_tarski @ A @ B ) & ( r1_tarski @ B @ C ) ) => ( r1_tarski @ A @ C ) ) ),file(xboole_1,t1_xboole_1)).
thf(t2_boole,axiom,( ! [A: $i] : ( = @ ( k3_xboole_0 @ A @ k1_xboole_0 ) @ k1_xboole_0 ) ),file(boole,t2_boole)).
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(t3_xboole_1,axiom,( ! [A: $i] : ( ( r1_tarski @ A @ k1_xboole_0 ) => ( = @ A @ k1_xboole_0 ) ) ),file(xboole_1,t3_xboole_1)).
thf(t4_fraenkel,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( r1_tarski @ C @ B ) & ( r1_tarski @ D @ A ) ) => ( ( = @ ( k1_funct_2 @ C @ D ) @ k1_xboole_0 ) | ! [E: $i] : ( ( m1_subset_1 @ E @ ( k1_funct_2 @ C @ D ) ) => ? [F: $i] : ( ( m2_funct_2 @ F @ B @ A @ ( k9_funct_2 @ B @ A ) ) & ( = @ ( k2_partfun1 @ B @ A @ F @ C ) @ E ) ) ) ) ) ) ),file(fraenkel,t4_fraenkel)).
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_fraenkel,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( m2_funct_2 @ D @ C @ A @ ( k9_funct_2 @ C @ A ) ) => ( r2_relset_1 @ C @ A @ ( k2_partfun1 @ C @ A @ D @ B ) @ ( k2_partfun1 @ C @ A @ D @ ( k3_xboole_0 @ C @ B ) ) ) ) ) ),file(fraenkel,t5_fraenkel)).
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(t61_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ B ) => ( = @ ( k9_xtuple_0 @ ( k5_relat_1 @ B @ A ) ) @ ( k3_xboole_0 @ ( k9_xtuple_0 @ B ) @ A ) ) ) ),file(relat_1,t61_relat_1)).
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(t8_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_funct_1 @ C ) & ( v1_funct_2 @ C @ A @ B ) & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) => ( ( ( = @ B @ k1_xboole_0 ) => ( = @ A @ k1_xboole_0 ) ) => ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ) ),file(funct_2,t8_funct_2)).
thf(s3_funct_2,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ( ! [D: $i] : ( ( m1_subset_1 @ D @ C ) => ? [E: $i] : ( ( m1_subset_1 @ E @ B ) & ( A @ D @ E ) ) ) => ? [D: $i] : ( ( v1_funct_1 @ D ) & ( v1_funct_2 @ D @ C @ B ) & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ C @ B ) ) ) & ! [E: $i] : ( ( m1_subset_1 @ E @ C ) => ( A @ E @ ( k3_funct_2 @ C @ B @ D @ E ) ) ) ) ) ),file(funct_2,s3_funct_2)).
thf(s25_fraenkel,conjecture,( ( ( v1_finset_1 @ f3_s25_fraenkel ) & ( v1_finset_1 @ f4_s25_fraenkel ) & ! [A: $i] : ( ( m2_funct_2 @ A @ f1_s25_fraenkel @ f2_s25_fraenkel @ ( k9_funct_2 @ f1_s25_fraenkel @ f2_s25_fraenkel ) ) => ! [B: $i] : ( ( m2_funct_2 @ B @ f1_s25_fraenkel @ f2_s25_fraenkel @ ( k9_funct_2 @ f1_s25_fraenkel @ f2_s25_fraenkel ) ) => ( ( r2_relset_1 @ f1_s25_fraenkel @ f2_s25_fraenkel @ ( k2_partfun1 @ f1_s25_fraenkel @ f2_s25_fraenkel @ A @ f3_s25_fraenkel ) @ ( k2_partfun1 @ f1_s25_fraenkel @ f2_s25_fraenkel @ B @ f3_s25_fraenkel ) ) => ( = @ ( f5_s25_fraenkel @ A ) @ ( f5_s25_fraenkel @ B ) ) ) ) ) ) => ( v1_finset_1 @ ( replSep1 @ ^ [A: $i] : ( m2_funct_2 @ A @ f1_s25_fraenkel @ f2_s25_fraenkel @ ( k9_funct_2 @ f1_s25_fraenkel @ f2_s25_fraenkel ) ) @ ^ [A: $i] : ( f5_s25_fraenkel @ A ) @ ^ [A: $i] : ( r1_tarski @ ( k7_relset_1 @ f1_s25_fraenkel @ f2_s25_fraenkel @ A @ f3_s25_fraenkel ) @ f4_s25_fraenkel ) ) ) ),file(fraenkel,s25_fraenkel)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
