% Mizar problem: e2_37_1_2,card_lar,832,66 
include('Axioms/SET010^1.ax').
thf(c1_37_type,type,( c1_37__card_lar: $i )).
thf(c1_37_1_2_type,type,( c1_37_1_2__card_lar: $i )).
thf(c2_37_type,type,( c2_37__card_lar: $i )).
thf(k1_card_1_type,type,( k1_card_1: $i > $i )).
thf(k1_card_lar_type,type,( k1_card_lar: $i > $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(m1_card_lar_type,type,( m1_card_lar: $i > $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $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_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_card_1_type,type,( v3_card_1: $i > $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v4_card_3_type,type,( v4_card_3: $i > $o )).
thf(v4_ordinal1_type,type,( v4_ordinal1: $i > $o )).
thf(v5_card_3_type,type,( v5_card_3: $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(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(rc1_card_5,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(card_5,rc1_card_5)).
thf(rc2_card_1,axiom,( ? [A: $i] : ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) ),file(card_1,rc2_card_1)).
thf(rc2_card_lar,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) & ~ ( v4_card_3 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ A ) & ( v1_ordinal1 @ B ) & ( v2_ordinal1 @ B ) & ( v3_ordinal1 @ B ) & ~ ( v1_finset_1 @ B ) & ( v1_card_1 @ B ) ) ) ),file(card_lar,rc2_card_lar)).
thf(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(cc10_ordinal1,axiom,( ! [A: $i] : ( ( v6_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v6_ordinal1 @ B ) ) ) ),file(ordinal1,cc10_ordinal1)).
thf(cc1_card_lar,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) => ( ( v3_ordinal1 @ A ) & ( v4_ordinal1 @ A ) ) ) ),file(card_lar,cc1_card_lar)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc2_card_lar,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v4_ordinal1 @ A ) & ~ ( v1_xboole_0 @ A ) ) => ( ( v3_ordinal1 @ A ) & ~ ( v1_finset_1 @ A ) ) ) ),file(card_lar,cc2_card_lar)).
thf(cc3_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_card_1 @ A ) ) ),file(card_1,cc3_card_1)).
thf(cc4_card_3,axiom,( ! [A: $i] : ( ( v5_card_3 @ A ) => ( ~ ( v1_finset_1 @ A ) & ( v4_card_3 @ A ) ) ) ),file(card_3,cc4_card_3)).
thf(cc5_card_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_finset_1 @ A ) ) ),file(card_1,cc5_card_1)).
thf(cc5_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(cc6_card_1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v1_finset_1 @ A ) ) => ( v7_ordinal1 @ A ) ) ),file(card_1,cc6_card_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc7_card_1,axiom,( ! [A: $i] : ( ( v3_card_1 @ A @ k1_xboole_0 ) => ( v1_xboole_0 @ A ) ) ),file(card_1,cc7_card_1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc5_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ? [B: $i] : ( v3_card_1 @ B @ A ) ) ),file(card_1,rc5_card_1)).
thf(rc5_card_3,axiom,( ? [A: $i] : ( v5_card_3 @ A ) ),file(card_3,rc5_card_3)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(projectivity_k1_card_1,axiom,( ! [A: $i] : ( = @ ( k1_card_1 @ ( k1_card_1 @ A ) ) @ ( k1_card_1 @ A ) ) ),file(card_1,k1_card_1)).
thf(reflexivity_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( r1_ordinal1 @ A @ A ) ) ),file(ordinal1,r1_ordinal1)).
thf(connectedness_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) | ( r1_ordinal1 @ B @ A ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_m1_card_lar,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m1_card_lar @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(card_lar,m1_card_lar)).
thf(redefinition_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) <=> ( r1_tarski @ A @ B ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(dt_k1_card_1,axiom,( ! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ) ),file(card_1,k1_card_1)).
thf(dt_k1_card_lar,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v3_ordinal1 @ A ) & ( v4_ordinal1 @ A ) & ~ ( v1_finset_1 @ A ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ( v3_ordinal1 @ C ) ) => ( m1_subset_1 @ ( k1_card_lar @ A @ B @ C ) @ B ) ) ),file(card_lar,k1_card_lar)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_m1_card_lar,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m1_card_lar @ C @ A @ B ) => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ) ),file(card_lar,m1_card_lar)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_37__card_lar,axiom,( ~ ( v1_finset_1 @ c1_37__card_lar ) & ( v1_card_1 @ c1_37__card_lar ) & ~ ( v4_card_3 @ c1_37__card_lar ) ),file(card_lar,c1_37__card_lar)).
thf(dt_c1_37_1_2__card_lar,axiom,( m1_subset_1 @ c1_37_1_2__card_lar @ c1_37__card_lar ),file(card_lar,c1_37_1_2__card_lar)).
thf(dt_c2_37__card_lar,axiom,( ~ ( v1_xboole_0 @ c2_37__card_lar ) & ( m1_subset_1 @ c2_37__card_lar @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ c1_37__card_lar ) ) ) ),file(card_lar,c2_37__card_lar)).
thf(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(cc1_card_2,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v1_card_1 @ A ) ) => ( ( v4_ordinal1 @ A ) & ( v1_card_1 @ A ) ) ) ),file(card_2,cc1_card_2)).
thf(cc1_card_5,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(card_5,cc1_card_5)).
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(cc5_card_3,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v4_card_3 @ A ) ) => ( v5_card_3 @ A ) ) ),file(card_3,cc5_card_3)).
thf(cc6_card_3,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v4_card_3 @ A ) ) ),file(card_3,cc6_card_3)).
thf(cc7_card_3,axiom,( ! [A: $i] : ( ( v4_card_3 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_card_3 @ B ) ) ) ),file(card_3,cc7_card_3)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc8_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_card_1 @ A @ k1_xboole_0 ) ) ),file(card_1,cc8_card_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc1_card_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( ( v1_xboole_0 @ ( k1_card_1 @ A ) ) & ( v1_card_1 @ ( k1_card_1 @ A ) ) ) ) ),file(card_1,fc1_card_1)).
thf(fc2_card_1,axiom,( ! [A: $i] : ( ~ ( v1_xboole_0 @ A ) => ( ~ ( v1_xboole_0 @ ( k1_card_1 @ A ) ) & ( v1_card_1 @ ( k1_card_1 @ A ) ) ) ) ),file(card_1,fc2_card_1)).
thf(fc6_card_1,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( ( v1_finset_1 @ ( k1_card_1 @ A ) ) & ( v1_card_1 @ ( k1_card_1 @ A ) ) ) ) ),file(card_1,fc6_card_1)).
thf(fc8_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ( ~ ( v1_finset_1 @ ( k1_card_1 @ A ) ) & ( v1_card_1 @ ( k1_card_1 @ A ) ) ) ) ),file(card_1,fc8_card_1)).
thf(fc9_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ) ),file(card_1,fc9_card_1)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
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(rc3_card_1,axiom,( ? [A: $i] : ~ ( v1_finset_1 @ A ) ),file(card_1,rc3_card_1)).
thf(rc4_card_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) & ~ ( v1_finset_1 @ B ) ) ) ),file(card_1,rc4_card_1)).
thf(s2_trees_2,axiom,( ! [A: $i] : ! [B: $i > $i] : ! [C: $i] : ( r1_ordinal1 @ ( k1_card_1 @ ( replSep1 @ ^ [D: $i] : ( m1_subset_1 @ D @ C ) @ ^ [D: $i] : ( B @ D ) @ ^ [D: $i] : ( r2_hidden @ D @ A ) ) ) @ ( k1_card_1 @ A ) ) ),file(trees_2,s2_trees_2)).
thf(e2_37_1_2__card_lar,conjecture,( r1_ordinal1 @ ( k1_card_1 @ ( replSep1 @ ^ [A: $i] : ( m1_card_lar @ A @ c1_37__card_lar @ c2_37__card_lar ) @ ^ [A: $i] : ( k1_card_lar @ c1_37__card_lar @ A @ c1_37_1_2__card_lar ) @ ^ [A: $i] : ( r2_hidden @ A @ c2_37__card_lar ) ) ) @ ( k1_card_1 @ c2_37__card_lar ) ),file(card_lar,e2_37_1_2__card_lar)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
