% Mizar problem: e2_1_1_2,functor0,75,43 
include('Axioms/SET010^1.ax').
thf(c1_1_1_type,type,( c1_1_1__functor0: $i )).
thf(f1_s1_functor0_type,type,( f1_s1_functor0: $i )).
thf(f2_s1_functor0_type,type,( f2_s1_functor0: $i )).
thf(f5_s1_functor0_type,type,( f5_s1_functor0: $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_xtuple_0_type,type,( k1_xtuple_0: $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(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(p1_s1_functor0_type,type,( p1_s1_functor0: $i > $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_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_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_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
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(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(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(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(fc19_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc19_funct_1)).
thf(fc8_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ A @ B ) ) ) ) ),file(funcop_1,fc8_funcop_1)).
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(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_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_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(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(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(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
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(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_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_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(cc7_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v4_funct_1 @ A ) ) ),file(funct_1,cc7_funct_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(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_1)).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(rd3_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xtuple_0 @ A ) => ( = @ ( k4_tarski @ ( k1_xtuple_0 @ A ) @ ( k2_xtuple_0 @ A ) ) @ A ) ) ),file(xtuple_0,rd3_xtuple_0)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_xtuple_0,axiom,( $true ),file(xtuple_0,k1_xtuple_0)).
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_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_1_1__functor0,axiom,( m1_subset_1 @ c1_1_1__functor0 @ ( k2_zfmisc_1 @ f1_s1_functor0 @ f1_s1_functor0 ) ),file(functor0,c1_1_1__functor0)).
thf(dt_f1_s1_functor0,axiom,( ~ ( v1_xboole_0 @ f1_s1_functor0 ) ),file(functor0,f1_s1_functor0)).
thf(dt_f2_s1_functor0,axiom,( ( v1_relat_1 @ f2_s1_functor0 ) & ( v1_funct_1 @ f2_s1_functor0 ) ),file(functor0,f2_s1_functor0)).
thf(dt_f5_s1_functor0,axiom,( $true ),file(functor0,f5_s1_functor0)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_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(rd1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k1_xtuple_0 @ ( k4_tarski @ A @ B ) ) @ A ) ),file(xtuple_0,rd1_xtuple_0)).
thf(rd2_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xtuple_0 @ ( k4_tarski @ A @ B ) ) @ B ) ),file(xtuple_0,rd2_xtuple_0)).
thf(e1_1_1__functor0,axiom,( = @ f2_s1_functor0 @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ ( k2_zfmisc_1 @ f1_s1_functor0 @ f1_s1_functor0 ) ) @ ^ [A: $i] : ( k4_tarski @ A @ ( f5_s1_functor0 @ ( k1_xtuple_0 @ A ) @ ( k2_xtuple_0 @ A ) ) ) @ ^ [A: $i] : ( p1_s1_functor0 @ ( k1_xtuple_0 @ A ) @ ( k2_xtuple_0 @ A ) ) ) ),file(functor0,e1_1_1__functor0)).
thf(e4_1_1__functor0,axiom,( p1_s1_functor0 @ ( k1_xtuple_0 @ c1_1_1__functor0 ) @ ( k2_xtuple_0 @ c1_1_1__functor0 ) ),file(functor0,e4_1_1__functor0)).
thf(s3_altcat_2,axiom,( ! [A: $i] : ! [B: $i > $o] : ! [C: $i > $i] : ! [D: $i] : ! [E: $i] : ( ( ( = @ E @ ( replSep1 @ ^ [F: $i] : ( m1_subset_1 @ F @ D ) @ ^ [F: $i] : ( k4_tarski @ F @ ( C @ F ) ) @ ^ [F: $i] : ( B @ F ) ) ) & ( B @ A ) ) => ( = @ ( k1_funct_1 @ E @ A ) @ ( C @ A ) ) ) ),file(altcat_2,s3_altcat_2)).
thf(e2_1_1_2__functor0,conjecture,( = @ ( k1_funct_1 @ f2_s1_functor0 @ c1_1_1__functor0 ) @ ( f5_s1_functor0 @ ( k1_xtuple_0 @ c1_1_1__functor0 ) @ ( k2_xtuple_0 @ c1_1_1__functor0 ) ) ),file(functor0,e2_1_1_2__functor0)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
