% Mizar problem: e3_47,card_1,1083,11 
include('Axioms/SET010^0.ax').
thf(c2_47_type,type,( c2_47__card_1: $i )).
thf(k1_ordinal1_type,type,( k1_ordinal1: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(r2_tarski_type,type,( r2_tarski: $i > $i > $o )).
thf(r2_wellord2_type,type,( r2_wellord2: $i > $i > $o )).
thf(v1_card_1_type,type,( v1_card_1: $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_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_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_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(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_zfmisc_1,axiom,( ! [A: $i] : ( ~ ( v1_zfmisc_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(zfmisc_1,cc2_zfmisc_1)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
thf(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_1)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_zfmisc_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_zfmisc_1 @ A ) ) ),file(zfmisc_1,rc1_zfmisc_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(rc2_zfmisc_1,axiom,( ? [A: $i] : ~ ( v1_zfmisc_1 @ A ) ),file(zfmisc_1,rc2_zfmisc_1)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_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(cc1_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc1_finset_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(cc1_zfmisc_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_zfmisc_1 @ A ) ) ),file(zfmisc_1,cc1_zfmisc_1)).
thf(cc2_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc2_card_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc6_finset_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_finset_1 @ A ) ) ),file(finset_1,cc6_finset_1)).
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_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(symmetry_r2_wellord2,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_wellord2 @ A @ B ) => ( r2_wellord2 @ B @ A ) ) ),file(wellord2,r2_wellord2)).
thf(reflexivity_r2_wellord2,axiom,( ! [A: $i] : ! [B: $i] : ( r2_wellord2 @ A @ A ) ),file(wellord2,r2_wellord2)).
thf(redefinition_r2_wellord2,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_wellord2 @ A @ B ) <=> ( r2_tarski @ A @ B ) ) ),file(wellord2,r2_wellord2)).
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_c2_47__card_1,axiom,( v7_ordinal1 @ c2_47__card_1 ),file(card_1,c2_47__card_1)).
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(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(e2_47__card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( r2_wellord2 @ A @ k1_xboole_0 ) => ( = @ A @ k1_xboole_0 ) ) ) ),file(card_1,e2_47__card_1)).
thf(e1_47__card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ! [B: $i] : ( ( v7_ordinal1 @ B ) => ( ( r2_wellord2 @ B @ A ) => ( = @ B @ A ) ) ) => ! [B: $i] : ( ( v7_ordinal1 @ B ) => ( ( r2_wellord2 @ B @ ( k1_ordinal1 @ A ) ) => ( = @ B @ ( k1_ordinal1 @ A ) ) ) ) ) ) ),file(card_1,e1_47__card_1)).
thf(s17_ordinal2,axiom,( ! [A: $i] : ! [B: $i > $o] : ( ( ( B @ k1_xboole_0 ) & ! [C: $i] : ( ( v7_ordinal1 @ C ) => ( ( B @ C ) => ( B @ ( k1_ordinal1 @ C ) ) ) ) ) => ( B @ A ) ) ),file(ordinal2,s17_ordinal2)).
thf(e3_47__card_1,conjecture,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( r2_wellord2 @ A @ c2_47__card_1 ) => ( = @ A @ c2_47__card_1 ) ) ) ),file(card_1,e3_47__card_1)).
