% Mizar problem: e2_38_1,ordinal2,866,23 
include('Axioms/SET010^0.ax').
thf(f2_s5_ordinal2_type,type,( f2_s5_ordinal2: $i )).
thf(f3_s5_ordinal2_type,type,( f3_s5_ordinal2: $i > $i > $i )).
thf(f4_s5_ordinal2_type,type,( f4_s5_ordinal2: $i > $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_ordinal1_type,type,( k1_ordinal1: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k5_relat_1_type,type,( k5_relat_1: $i > $i > $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_ordinal2_type,type,( v1_ordinal2: $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(v4_ordinal1_type,type,( v4_ordinal1: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $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(cc1_funcop_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v1_funcop_1 @ B ) ) ) ) ),file(funcop_1,cc1_funcop_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(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(fc12_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) => ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc12_funct_1)).
thf(fc13_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v1_funcop_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(funcop_1,fc13_funcop_1)).
thf(fc13_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v3_funct_1 @ A ) ) => ~ ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc13_funct_1)).
thf(fc16_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v3_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v3_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(funcop_1,fc16_funcop_1)).
thf(fc17_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v4_funct_1 @ A ) & ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ C @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ C @ B ) ) ) ) ),file(funct_1,fc17_funct_1)).
thf(fc1_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v1_ordinal2 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(ordinal2,fc1_ordinal2)).
thf(fc2_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(ordinal2,fc2_ordinal2)).
thf(fc7_ordinal1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) => ( v7_ordinal1 @ ( k1_ordinal1 @ A ) ) ) ),file(ordinal1,fc7_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_ordinal2,axiom,( ? [A: $i] : ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) ),file(ordinal2,rc2_ordinal2)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_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(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( ( v5_ordinal1 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( ( v5_ordinal1 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_ordinal2 @ B ) ) ) ) ),file(ordinal2,cc1_ordinal2)).
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(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
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(rc1_ordinal2,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v4_ordinal1 @ A ) ) ),file(ordinal2,rc1_ordinal2)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
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_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc3_ordinal1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) ),file(ordinal1,rc3_ordinal1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
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_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_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_f2_s5_ordinal2,axiom,( $true ),file(ordinal2,f2_s5_ordinal2)).
thf(dt_f3_s5_ordinal2,axiom,( $true ),file(ordinal2,f3_s5_ordinal2)).
thf(dt_f4_s5_ordinal2,axiom,( $true ),file(ordinal2,f4_s5_ordinal2)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_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(fc2_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ~ ( v1_xboole_0 @ ( k1_ordinal1 @ A ) ) & ( v3_ordinal1 @ ( k1_ordinal1 @ A ) ) ) ) ),file(ordinal1,fc2_ordinal1)).
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(fc5_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v5_relat_1 @ ( k5_relat_1 @ A @ B ) @ ( k10_xtuple_0 @ A ) ) & ( v5_ordinal1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(ordinal1,fc5_ordinal1)).
thf(fc8_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(funct_1,fc8_funct_1)).
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(e1_38_1__ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ A ) => ? [C: $i] : ( ( v5_ordinal1 @ C ) & ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ( ( r2_hidden @ k1_xboole_0 @ B ) => ( = @ ( k1_funct_1 @ C @ k1_xboole_0 ) @ f2_s5_ordinal2 ) ) & ! [D: $i] : ( ( v3_ordinal1 @ D ) => ( ( r2_hidden @ ( k1_ordinal1 @ D ) @ B ) => ( = @ ( k1_funct_1 @ C @ ( k1_ordinal1 @ D ) ) @ ( f3_s5_ordinal2 @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) & ! [D: $i] : ( ( v3_ordinal1 @ D ) => ( ( ( r2_hidden @ D @ B ) & ( v4_ordinal1 @ D ) ) => ( ( = @ D @ k1_xboole_0 ) | ( = @ ( k1_funct_1 @ C @ D ) @ ( f4_s5_ordinal2 @ D @ ( k5_relat_1 @ C @ D ) ) ) ) ) ) ) ) ) => ? [B: $i] : ( ( v5_ordinal1 @ B ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( = @ ( k9_xtuple_0 @ B ) @ A ) & ( ( r2_hidden @ k1_xboole_0 @ A ) => ( = @ ( k1_funct_1 @ B @ k1_xboole_0 ) @ f2_s5_ordinal2 ) ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( r2_hidden @ ( k1_ordinal1 @ C ) @ A ) => ( = @ ( k1_funct_1 @ B @ ( k1_ordinal1 @ C ) ) @ ( f3_s5_ordinal2 @ C @ ( k1_funct_1 @ B @ C ) ) ) ) ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( ( r2_hidden @ C @ A ) & ( v4_ordinal1 @ C ) ) => ( ( = @ C @ k1_xboole_0 ) | ( = @ ( k1_funct_1 @ B @ C ) @ ( f4_s5_ordinal2 @ C @ ( k5_relat_1 @ B @ C ) ) ) ) ) ) ) ) ) ),file(ordinal2,e1_38_1__ordinal2)).
thf(s2_ordinal1,axiom,( ! [A: $i > $o] : ( ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( r2_hidden @ C @ B ) => ( A @ C ) ) ) => ( A @ B ) ) ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( A @ B ) ) ) ),file(ordinal1,s2_ordinal1)).
thf(e2_38_1__ordinal2,conjecture,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ? [B: $i] : ( ( v5_ordinal1 @ B ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( = @ ( k9_xtuple_0 @ B ) @ A ) & ( ( r2_hidden @ k1_xboole_0 @ A ) => ( = @ ( k1_funct_1 @ B @ k1_xboole_0 ) @ f2_s5_ordinal2 ) ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( r2_hidden @ ( k1_ordinal1 @ C ) @ A ) => ( = @ ( k1_funct_1 @ B @ ( k1_ordinal1 @ C ) ) @ ( f3_s5_ordinal2 @ C @ ( k1_funct_1 @ B @ C ) ) ) ) ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( ( r2_hidden @ C @ A ) & ( v4_ordinal1 @ C ) ) => ( ( = @ C @ k1_xboole_0 ) | ( = @ ( k1_funct_1 @ B @ C ) @ ( f4_s5_ordinal2 @ C @ ( k5_relat_1 @ B @ C ) ) ) ) ) ) ) ) ),file(ordinal2,e2_38_1__ordinal2)).
