% Mizar problem: e1_29_1_1,parsp_1,385,10 
include('Axioms/SET010^0.ax').
thf(n1_type,type,( np__1: $i )).
thf(c1_29_type,type,( c1_29__parsp_1: $i )).
thf(k1_mcart_1_type,type,( k1_mcart_1: $i > $i > $i > $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(k2_mcart_1_type,type,( k2_mcart_1: $i > $i > $i > $i > $i )).
thf(k2_xtuple_0_type,type,( k2_xtuple_0: $i > $i )).
thf(k3_mcart_1_type,type,( k3_mcart_1: $i > $i > $i > $i > $i )).
thf(k3_zfmisc_1_type,type,( k3_zfmisc_1: $i > $i > $i > $i )).
thf(k4_struct_0_type,type,( k4_struct_0: $i > $i )).
thf(k4_xtuple_0_type,type,( k4_xtuple_0: $i > $i )).
thf(k4_zfmisc_1_type,type,( k4_zfmisc_1: $i > $i > $i > $i > $i )).
thf(k5_algstr_0_type,type,( k5_algstr_0: $i > $i > $i > $i )).
thf(k5_domain_1_type,type,( k5_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i )).
thf(k5_xtuple_0_type,type,( k5_xtuple_0: $i > $i )).
thf(k6_algstr_0_type,type,( k6_algstr_0: $i > $i > $i > $i )).
thf(k6_parsp_1_type,type,( k6_parsp_1: $i > $i )).
thf(k6_xtuple_0_type,type,( k6_xtuple_0: $i > $i > $i > $i > $i )).
thf(k8_group_1_type,type,( k8_group_1: $i > $i > $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(l1_algstr_0_type,type,( l1_algstr_0: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l2_algstr_0_type,type,( l2_algstr_0: $i > $o )).
thf(l2_struct_0_type,type,( l2_struct_0: $i > $o )).
thf(l3_algstr_0_type,type,( l3_algstr_0: $i > $o )).
thf(l3_struct_0_type,type,( l3_struct_0: $i > $o )).
thf(l4_algstr_0_type,type,( l4_algstr_0: $i > $o )).
thf(l4_struct_0_type,type,( l4_struct_0: $i > $o )).
thf(l5_algstr_0_type,type,( l5_algstr_0: $i > $o )).
thf(l6_algstr_0_type,type,( l6_algstr_0: $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(v13_algstr_0_type,type,( v13_algstr_0: $i > $o )).
thf(v13_struct_0_type,type,( v13_struct_0: $i > $i > $o )).
thf(v1_finset_1_type,type,( v1_finset_1: $i > $o )).
thf(v1_group_1_type,type,( v1_group_1: $i > $o )).
thf(v1_vectsp_1_type,type,( v1_vectsp_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_rlvect_1_type,type,( v2_rlvect_1: $i > $o )).
thf(v2_struct_0_type,type,( v2_struct_0: $i > $o )).
thf(v2_vectsp_1_type,type,( v2_vectsp_1: $i > $o )).
thf(v33_algstr_0_type,type,( v33_algstr_0: $i > $o )).
thf(v3_group_1_type,type,( v3_group_1: $i > $o )).
thf(v3_rlvect_1_type,type,( v3_rlvect_1: $i > $o )).
thf(v3_vectsp_1_type,type,( v3_vectsp_1: $i > $o )).
thf(v4_rlvect_1_type,type,( v4_rlvect_1: $i > $o )).
thf(v4_vectsp_1_type,type,( v4_vectsp_1: $i > $o )).
thf(v5_group_1_type,type,( v5_group_1: $i > $o )).
thf(v5_vectsp_1_type,type,( v5_vectsp_1: $i > $o )).
thf(v6_struct_0_type,type,( v6_struct_0: $i > $o )).
thf(v6_vectsp_1_type,type,( v6_vectsp_1: $i > $o )).
thf(v7_struct_0_type,type,( v7_struct_0: $i > $o )).
thf(v8_struct_0_type,type,( v8_struct_0: $i > $o )).
thf(v9_struct_0_type,type,( v9_struct_0: $i > $i > $o )).
thf(dt_l3_struct_0,axiom,( ! [A: $i] : ( ( l3_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l3_struct_0)).
thf(cc11_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ np__1 ) => ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ) ) ),file(struct_0,cc11_struct_0)).
thf(cc4_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v3_vectsp_1 @ A ) & ( v6_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_group_1 @ A ) ) ) ) ),file(vectsp_1,cc4_vectsp_1)).
thf(cc6_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( v6_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc6_vectsp_1)).
thf(rc4_vectsp_1,axiom,( ? [A: $i] : ( ( l4_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v1_group_1 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) ) ),file(vectsp_1,rc4_vectsp_1)).
thf(spc1_boole,axiom,( ~ ( v1_xboole_0 @ np__1 ) ),file(boole,spc1_boole)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_l1_algstr_0,axiom,( ! [A: $i] : ( ( l1_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l1_algstr_0)).
thf(dt_l4_algstr_0,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( l3_struct_0 @ A ) & ( l3_algstr_0 @ A ) ) ) ),file(algstr_0,l4_algstr_0)).
thf(dt_l4_struct_0,axiom,( ! [A: $i] : ( ( l4_struct_0 @ A ) => ( ( l2_struct_0 @ A ) & ( l3_struct_0 @ A ) ) ) ),file(struct_0,l4_struct_0)).
thf(cc10_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) => ( v13_struct_0 @ A @ np__1 ) ) ) ),file(struct_0,cc10_struct_0)).
thf(cc17_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc17_struct_0)).
thf(cc2_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v7_struct_0 @ A ) => ~ ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc2_struct_0)).
thf(cc3_struct_0,axiom,( ! [A: $i] : ( ( l4_struct_0 @ A ) => ( ~ ( v6_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc3_struct_0)).
thf(cc3_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v3_vectsp_1 @ A ) & ( v6_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc3_vectsp_1)).
thf(cc5_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ( ~ ( v2_struct_0 @ A ) & ~ ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc5_struct_0)).
thf(cc5_vectsp_1,axiom,( ! [A: $i] : ( ( l4_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_group_1 @ A ) ) ) ) ),file(vectsp_1,cc5_vectsp_1)).
thf(cc6_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v7_struct_0 @ A ) => ( v8_struct_0 @ A ) ) ) ),file(struct_0,cc6_struct_0)).
thf(cc7_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ~ ( v8_struct_0 @ A ) => ~ ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc7_struct_0)).
thf(cc9_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v13_struct_0 @ A @ k1_xboole_0 ) => ( v2_struct_0 @ A ) ) ) ),file(struct_0,cc9_struct_0)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc6_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc6_struct_0)).
thf(fc7_struct_0,axiom,( ! [A: $i] : ( ( ( v7_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc7_struct_0)).
thf(fc8_struct_0,axiom,( ! [A: $i] : ( ( ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc8_struct_0)).
thf(fc9_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v8_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc9_struct_0)).
thf(rc11_vectsp_1,axiom,( ? [A: $i] : ( ( l4_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) ),file(vectsp_1,rc11_vectsp_1)).
thf(rc17_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( v9_struct_0 @ B @ A ) ) ) ),file(struct_0,rc17_struct_0)).
thf(rc19_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v7_struct_0 @ A ) & ( l2_struct_0 @ A ) ) => ? [B: $i] : ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ~ ( v9_struct_0 @ B @ A ) ) ) ),file(struct_0,rc19_struct_0)).
thf(rc20_struct_0,axiom,( ? [A: $i] : ( ( l2_struct_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v7_struct_0 @ A ) ) ),file(struct_0,rc20_struct_0)).
thf(dt_k2_xtuple_0,axiom,( $true ),file(xtuple_0,k2_xtuple_0)).
thf(dt_k4_xtuple_0,axiom,( $true ),file(xtuple_0,k4_xtuple_0)).
thf(dt_k4_zfmisc_1,axiom,( $true ),file(zfmisc_1,k4_zfmisc_1)).
thf(dt_k5_xtuple_0,axiom,( $true ),file(xtuple_0,k5_xtuple_0)).
thf(dt_k6_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( l3_algstr_0 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k6_algstr_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),file(algstr_0,k6_algstr_0)).
thf(dt_k6_xtuple_0,axiom,( $true ),file(xtuple_0,k6_xtuple_0)).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_l2_algstr_0,axiom,( ! [A: $i] : ( ( l2_algstr_0 @ A ) => ( ( l2_struct_0 @ A ) & ( l1_algstr_0 @ A ) ) ) ),file(algstr_0,l2_algstr_0)).
thf(dt_l2_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l2_struct_0)).
thf(dt_l3_algstr_0,axiom,( ! [A: $i] : ( ( l3_algstr_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(algstr_0,l3_algstr_0)).
thf(dt_l5_algstr_0,axiom,( ! [A: $i] : ( ( l5_algstr_0 @ A ) => ( ( l4_algstr_0 @ A ) & ( l4_struct_0 @ A ) ) ) ),file(algstr_0,l5_algstr_0)).
thf(cc1_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v7_struct_0 @ A ) ) ) ),file(struct_0,cc1_struct_0)).
thf(cc2_vectsp_1,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v1_vectsp_1 @ A ) & ( v2_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v5_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc2_vectsp_1)).
thf(cc4_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( ( v2_struct_0 @ A ) & ( v8_struct_0 @ A ) ) ) ) ),file(struct_0,cc4_struct_0)).
thf(cc8_struct_0,axiom,( ! [A: $i] : ( ( l1_struct_0 @ A ) => ( ( v2_struct_0 @ A ) => ( v13_struct_0 @ A @ k1_xboole_0 ) ) ) ),file(struct_0,cc8_struct_0)).
thf(fc10_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( v9_struct_0 @ ( k4_struct_0 @ A ) @ A ) ) ),file(struct_0,fc10_struct_0)).
thf(fc11_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) ) => ~ ( v1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ),file(subset_1,fc11_subset_1)).
thf(fc12_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) ) => ~ ( v1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),file(subset_1,fc12_subset_1)).
thf(fc1_struct_0,axiom,( ! [A: $i] : ( ( ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc1_struct_0)).
thf(fc2_struct_0,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( l1_struct_0 @ A ) ) => ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,fc2_struct_0)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_vectsp_1,axiom,( ? [A: $i] : ( ( l5_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v4_vectsp_1 @ A ) ) ),file(vectsp_1,rc2_vectsp_1)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc3_vectsp_1,axiom,( ? [A: $i] : ( ( l3_algstr_0 @ A ) & ~ ( v2_struct_0 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) ) ),file(vectsp_1,rc3_vectsp_1)).
thf(commutativity_k8_group_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( l3_algstr_0 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ( = @ ( k8_group_1 @ A @ B @ C ) @ ( k8_group_1 @ A @ C @ B ) ) ) ),file(group_1,k8_group_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k1_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) => ( = @ ( k1_mcart_1 @ A @ B @ C @ D ) @ ( k4_xtuple_0 @ D ) ) ) ),file(mcart_1,k1_mcart_1)).
thf(redefinition_k2_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) => ( = @ ( k2_mcart_1 @ A @ B @ C @ D ) @ ( k5_xtuple_0 @ D ) ) ) ),file(mcart_1,k2_mcart_1)).
thf(redefinition_k3_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) => ( = @ ( k3_mcart_1 @ A @ B @ C @ D ) @ ( k2_xtuple_0 @ D ) ) ) ),file(mcart_1,k3_mcart_1)).
thf(redefinition_k5_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ! [G: $i] : ! [H: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) & ( m1_subset_1 @ G @ C ) & ( m1_subset_1 @ H @ D ) ) => ( = @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k6_xtuple_0 @ E @ F @ G @ H ) ) ) ),file(domain_1,k5_domain_1)).
thf(redefinition_k8_group_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( l3_algstr_0 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ( = @ ( k8_group_1 @ A @ B @ C ) @ ( k6_algstr_0 @ A @ B @ C ) ) ) ),file(group_1,k8_group_1)).
thf(dt_k1_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) => ( m1_subset_1 @ ( k1_mcart_1 @ A @ B @ C @ D ) @ A ) ) ),file(mcart_1,k1_mcart_1)).
thf(dt_k2_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) => ( m1_subset_1 @ ( k2_mcart_1 @ A @ B @ C @ D ) @ B ) ) ),file(mcart_1,k2_mcart_1)).
thf(dt_k3_mcart_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) => ( m1_subset_1 @ ( k3_mcart_1 @ A @ B @ C @ D ) @ C ) ) ),file(mcart_1,k3_mcart_1)).
thf(dt_k3_zfmisc_1,axiom,( $true ),file(zfmisc_1,k3_zfmisc_1)).
thf(dt_k4_struct_0,axiom,( ! [A: $i] : ( ( l2_struct_0 @ A ) => ( m1_subset_1 @ ( k4_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),file(struct_0,k4_struct_0)).
thf(dt_k5_algstr_0,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( l2_algstr_0 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k5_algstr_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),file(algstr_0,k5_algstr_0)).
thf(dt_k5_domain_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ! [E: $i] : ! [F: $i] : ! [G: $i] : ! [H: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ~ ( v1_xboole_0 @ C ) & ~ ( v1_xboole_0 @ D ) & ( m1_subset_1 @ E @ A ) & ( m1_subset_1 @ F @ B ) & ( m1_subset_1 @ G @ C ) & ( m1_subset_1 @ H @ D ) ) => ( m1_subset_1 @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),file(domain_1,k5_domain_1)).
thf(dt_k6_parsp_1,axiom,( $true ),file(parsp_1,k6_parsp_1)).
thf(dt_k8_group_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ~ ( v2_struct_0 @ A ) & ( v5_group_1 @ A ) & ( l3_algstr_0 @ A ) & ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) & ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) ) => ( m1_subset_1 @ ( k8_group_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),file(group_1,k8_group_1)).
thf(dt_l6_algstr_0,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( l2_algstr_0 @ A ) & ( l5_algstr_0 @ A ) ) ) ),file(algstr_0,l6_algstr_0)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_c1_29__parsp_1,axiom,( ~ ( v2_struct_0 @ c1_29__parsp_1 ) & ~ ( v6_struct_0 @ c1_29__parsp_1 ) & ( v13_algstr_0 @ c1_29__parsp_1 ) & ( v33_algstr_0 @ c1_29__parsp_1 ) & ( v3_group_1 @ c1_29__parsp_1 ) & ( v5_group_1 @ c1_29__parsp_1 ) & ( v4_vectsp_1 @ c1_29__parsp_1 ) & ( v5_vectsp_1 @ c1_29__parsp_1 ) & ( v2_rlvect_1 @ c1_29__parsp_1 ) & ( v3_rlvect_1 @ c1_29__parsp_1 ) & ( v4_rlvect_1 @ c1_29__parsp_1 ) & ( l6_algstr_0 @ c1_29__parsp_1 ) ),file(parsp_1,c1_29__parsp_1)).
thf(cc1_vectsp_1,axiom,( ! [A: $i] : ( ( l6_algstr_0 @ A ) => ( ( ~ ( v2_struct_0 @ A ) & ( v5_vectsp_1 @ A ) ) => ( ~ ( v2_struct_0 @ A ) & ( v1_vectsp_1 @ A ) & ( v2_vectsp_1 @ A ) ) ) ) ),file(vectsp_1,cc1_vectsp_1)).
thf(fc2_parsp_1,axiom,( ! [A: $i] : ( ( ~ ( v2_struct_0 @ A ) & ~ ( v6_struct_0 @ A ) & ( v13_algstr_0 @ A ) & ( v33_algstr_0 @ A ) & ( v3_group_1 @ A ) & ( v5_group_1 @ A ) & ( v4_vectsp_1 @ A ) & ( v5_vectsp_1 @ A ) & ( v2_rlvect_1 @ A ) & ( v3_rlvect_1 @ A ) & ( v4_rlvect_1 @ A ) & ( l6_algstr_0 @ A ) ) => ~ ( v1_xboole_0 @ ( k6_parsp_1 @ A ) ) ) ),file(parsp_1,fc2_parsp_1)).
thf(s1_xboole_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ? [C: $i] : ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( r2_hidden @ D @ B ) & ( A @ D ) ) ) ),file(xboole_0,s1_xboole_0)).
thf(e1_29_1_1__parsp_1,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ ( k6_parsp_1 @ c1_29__parsp_1 ) ) & ? [C: $i] : ( ( m1_subset_1 @ C @ ( k3_zfmisc_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) ) ) & ? [D: $i] : ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) ) ) & ? [E: $i] : ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) ) ) & ? [F: $i] : ( ( m1_subset_1 @ F @ ( k3_zfmisc_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) ) ) & ( = @ B @ ( k5_domain_1 @ ( k3_zfmisc_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) ) @ ( k3_zfmisc_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) ) @ ( k3_zfmisc_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) ) @ ( k3_zfmisc_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) ) @ C @ D @ E @ F ) ) & ( = @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k8_group_1 @ c1_29__parsp_1 @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k1_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ C ) @ ( k1_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ D ) ) @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k2_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ E ) @ ( k2_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ F ) ) ) @ ( k8_group_1 @ c1_29__parsp_1 @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k1_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ E ) @ ( k1_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ F ) ) @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k2_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ C ) @ ( k2_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ D ) ) ) ) @ ( k4_struct_0 @ c1_29__parsp_1 ) ) & ( = @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k8_group_1 @ c1_29__parsp_1 @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k1_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ C ) @ ( k1_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ D ) ) @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k3_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ E ) @ ( k3_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ F ) ) ) @ ( k8_group_1 @ c1_29__parsp_1 @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k1_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ E ) @ ( k1_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ F ) ) @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k3_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ C ) @ ( k3_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ D ) ) ) ) @ ( k4_struct_0 @ c1_29__parsp_1 ) ) & ( = @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k8_group_1 @ c1_29__parsp_1 @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k2_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ C ) @ ( k2_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ D ) ) @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k3_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ E ) @ ( k3_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ F ) ) ) @ ( k8_group_1 @ c1_29__parsp_1 @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k2_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ E ) @ ( k2_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ F ) ) @ ( k5_algstr_0 @ c1_29__parsp_1 @ ( k3_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ C ) @ ( k3_mcart_1 @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ ( u1_struct_0 @ c1_29__parsp_1 ) @ D ) ) ) ) @ ( k4_struct_0 @ c1_29__parsp_1 ) ) ) ) ) ) ) ) ),file(parsp_1,e1_29_1_1__parsp_1)).
