% Mizar problem: e4_92_1,ordinal2,2464,21 
include('Axioms/SET010^0.ax').
thf(f1_s20_ordinal2_type,type,( f1_s20_ordinal2: $i )).
thf(f2_s20_ordinal2_type,type,( f2_s20_ordinal2: $i > $i > $i )).
thf(f3_s20_ordinal2_type,type,( f3_s20_ordinal2: $i )).
thf(f4_s20_ordinal2_type,type,( f4_s20_ordinal2: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_ordinal1_type,type,( k1_ordinal1: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(v1_funcop_1_type,type,( v1_funcop_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $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_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_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $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(fc18_funct_1,axiom,( ! [A: $i] : ( ( ~ ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(funct_1,fc18_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(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
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(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
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_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
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_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(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc2_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ~ ( v1_xboole_0 @ ( k1_ordinal1 @ A ) ) & ( v3_ordinal1 @ ( k1_ordinal1 @ A ) ) ) ) ),file(ordinal1,fc2_ordinal1)).
thf(fc7_ordinal1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) => ( v7_ordinal1 @ ( k1_ordinal1 @ A ) ) ) ),file(ordinal1,fc7_ordinal1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
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(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_ordinal1,axiom,( $true ),file(ordinal1,k1_ordinal1)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_f1_s20_ordinal2,axiom,( $true ),file(ordinal2,f1_s20_ordinal2)).
thf(dt_f2_s20_ordinal2,axiom,( $true ),file(ordinal2,f2_s20_ordinal2)).
thf(dt_f3_s20_ordinal2,axiom,( ( v1_relat_1 @ f3_s20_ordinal2 ) & ( v1_funct_1 @ f3_s20_ordinal2 ) ),file(ordinal2,f3_s20_ordinal2)).
thf(dt_f4_s20_ordinal2,axiom,( ( v1_relat_1 @ f4_s20_ordinal2 ) & ( v1_funct_1 @ f4_s20_ordinal2 ) ),file(ordinal2,f4_s20_ordinal2)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(fc1_ordinal1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_ordinal1 @ A ) ) ),file(ordinal1,fc1_ordinal1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(e1_92__ordinal2,axiom,( = @ ( k9_xtuple_0 @ f3_s20_ordinal2 ) @ k4_ordinal1 ),file(ordinal2,e1_92__ordinal2)).
thf(e2_92__ordinal2,axiom,( = @ ( k1_funct_1 @ f3_s20_ordinal2 @ k1_xboole_0 ) @ f1_s20_ordinal2 ),file(ordinal2,e2_92__ordinal2)).
thf(e3_92_1__ordinal2,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( = @ ( k1_funct_1 @ f3_s20_ordinal2 @ ( k1_ordinal1 @ A ) ) @ ( f2_s20_ordinal2 @ A @ ( k1_funct_1 @ f3_s20_ordinal2 @ A ) ) ) ) ),file(ordinal2,e3_92_1__ordinal2)).
thf(e4_92__ordinal2,axiom,( = @ ( k9_xtuple_0 @ f4_s20_ordinal2 ) @ k4_ordinal1 ),file(ordinal2,e4_92__ordinal2)).
thf(e5_92__ordinal2,axiom,( = @ ( k1_funct_1 @ f4_s20_ordinal2 @ k1_xboole_0 ) @ f1_s20_ordinal2 ),file(ordinal2,e5_92__ordinal2)).
thf(e1_92_1__ordinal2,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( = @ ( k1_funct_1 @ f4_s20_ordinal2 @ ( k1_ordinal1 @ A ) ) @ ( f2_s20_ordinal2 @ A @ ( k1_funct_1 @ f4_s20_ordinal2 @ A ) ) ) ) ),file(ordinal2,e1_92_1__ordinal2)).
thf(e2_92_1__ordinal2,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( = @ C @ ( f2_s20_ordinal2 @ A @ B ) ) & ( = @ D @ ( f2_s20_ordinal2 @ A @ B ) ) ) => ( = @ C @ D ) ) ) ),file(ordinal2,e2_92_1__ordinal2)).
thf(s19_ordinal2,axiom,( ! [A: $i > $i > $i > $o] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) ) => ( ( ( = @ ( k9_xtuple_0 @ D ) @ k4_ordinal1 ) & ( = @ ( k1_funct_1 @ D @ k1_xboole_0 ) @ B ) & ! [E: $i] : ( ( v7_ordinal1 @ E ) => ( A @ E @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ D @ ( k1_ordinal1 @ E ) ) ) ) & ( = @ ( k9_xtuple_0 @ C ) @ k4_ordinal1 ) & ( = @ ( k1_funct_1 @ C @ k1_xboole_0 ) @ B ) & ! [E: $i] : ( ( v7_ordinal1 @ E ) => ( A @ E @ ( k1_funct_1 @ C @ E ) @ ( k1_funct_1 @ C @ ( k1_ordinal1 @ E ) ) ) ) & ! [E: $i] : ( ( v7_ordinal1 @ E ) => ! [F: $i] : ! [G: $i] : ! [H: $i] : ( ( ( A @ E @ F @ G ) & ( A @ E @ F @ H ) ) => ( = @ G @ H ) ) ) ) => ( = @ D @ C ) ) ) ),file(ordinal2,s19_ordinal2)).
thf(e4_92_1__ordinal2,conjecture,( = @ f3_s20_ordinal2 @ f4_s20_ordinal2 ),file(ordinal2,e4_92_1__ordinal2)).
