% Mizar problem: e4_85_6_1,orders_1,1736,53 
include('Axioms/SET010^1.ax').
thf(c1_85_type,type,( c1_85__orders_1: $i )).
thf(c1_85_6_1_type,type,( c1_85_6_1__orders_1: $i )).
thf(c4_85_type,type,( c4_85__orders_1: $i )).
thf(c7_85_type,type,( c7_85__orders_1: $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(k4_tarski_type,type,( k4_tarski: $i > $i > $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(m1_subset_1_type,type,( m1_subset_1: $i > $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_orders_1_type,type,( v1_orders_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_relat_2_type,type,( v1_relat_2: $i > $o )).
thf(v1_setfam_1_type,type,( v1_setfam_1: $i > $o )).
thf(v1_wellord1_type,type,( v1_wellord1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v1_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(v1_zfmisc_1_type,type,( v1_zfmisc_1: $i > $o )).
thf(v2_finset_1_type,type,( v2_finset_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_orders_1_type,type,( v2_orders_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_relat_1_type,type,( v2_relat_1: $i > $o )).
thf(v2_relat_2_type,type,( v2_relat_2: $i > $o )).
thf(v2_wellord1_type,type,( v2_wellord1: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_orders_1_type,type,( v3_orders_1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v3_relat_1_type,type,( v3_relat_1: $i > $o )).
thf(v3_relat_2_type,type,( v3_relat_2: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_relat_2_type,type,( v4_relat_2: $i > $o )).
thf(v5_finset_1_type,type,( v5_finset_1: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(v5_relat_2_type,type,( v5_relat_2: $i > $o )).
thf(v6_ordinal1_type,type,( v6_ordinal1: $i > $o )).
thf(v6_relat_2_type,type,( v6_relat_2: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(v7_relat_2_type,type,( v7_relat_2: $i > $o )).
thf(v8_relat_2_type,type,( v8_relat_2: $i > $o )).
thf(cc2_wellord1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) & ( v4_relat_2 @ A ) & ( v6_relat_2 @ A ) & ( v8_relat_2 @ A ) & ( v1_wellord1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_wellord1 @ A ) ) ) ),file(wellord1,cc2_wellord1)).
thf(cc4_finset_1,axiom,( ! [A: $i] : ( ( v1_zfmisc_1 @ A ) => ( v1_finset_1 @ A ) ) ),file(finset_1,cc4_finset_1)).
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(fc24_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc24_relat_1)).
thf(fc25_relat_1,axiom,( ! [A: $i] : ( ( ( v1_zfmisc_1 @ A ) & ( v1_relat_1 @ A ) ) => ( v1_zfmisc_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc25_relat_1)).
thf(cc1_wellord1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_wellord1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) & ( v4_relat_2 @ A ) & ( v6_relat_2 @ A ) & ( v8_relat_2 @ A ) & ( v1_wellord1 @ A ) ) ) ),file(wellord1,cc1_wellord1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc2_relat_2,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_2 @ A ) & ( v8_relat_2 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) ) ) ),file(relat_2,cc2_relat_2)).
thf(cc3_partfun1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_2 @ A ) & ( v8_relat_2 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) ) ) ),file(partfun1,cc3_partfun1)).
thf(cc3_relat_2,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_relat_2 @ A ) & ( v8_relat_2 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v5_relat_2 @ A ) ) ) ),file(relat_2,cc3_relat_2)).
thf(cc4_relat_2,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v5_relat_2 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_2 @ A ) & ( v4_relat_2 @ A ) ) ) ),file(relat_2,cc4_relat_2)).
thf(cc5_finset_1,axiom,( ! [A: $i] : ( ~ ( v1_finset_1 @ A ) => ~ ( v1_zfmisc_1 @ A ) ) ),file(finset_1,cc5_finset_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(cc5_relat_2,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v7_relat_2 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) & ( v6_relat_2 @ A ) ) ) ),file(relat_2,cc5_relat_2)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(cc7_finset_1,axiom,( ! [A: $i] : ( ( v5_finset_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finset_1 @ B ) ) ) ),file(finset_1,cc7_finset_1)).
thf(cc8_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) ) ) ),file(funct_1,cc8_funct_1)).
thf(cc8_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) => ( ( v1_xboole_0 @ B ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) ) ) ) ),file(relat_1,cc8_relat_1)).
thf(fc10_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v1_setfam_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(funct_1,fc10_funct_1)).
thf(fc11_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( m1_subset_1 @ B @ ( k9_xtuple_0 @ A ) ) ) => ~ ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc11_funct_1)).
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_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(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(fc19_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_finset_1 @ A ) ) => ( v1_finset_1 @ ( k9_xtuple_0 @ A ) ) ) ),file(finset_1,fc19_finset_1)).
thf(fc19_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(funct_1,fc19_funct_1)).
thf(fc22_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_finset_1 @ A ) ) => ( v1_finset_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(finset_1,fc22_finset_1)).
thf(fc23_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v3_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(relat_1,fc23_relat_1)).
thf(fc26_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v1_finset_1 @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) & ( v1_finset_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ),file(finset_1,fc26_finset_1)).
thf(fc26_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ C @ A ) ) & ( v5_relat_1 @ ( k5_relat_1 @ C @ A ) @ B ) ) ) ),file(relat_1,fc26_relat_1)).
thf(fc27_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_finset_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) & ( v1_finset_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ),file(finset_1,fc27_finset_1)).
thf(fc35_finset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) => ( v1_finset_1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(finset_1,fc35_finset_1)).
thf(fc36_finset_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v2_finset_1 @ A ) ) => ( v5_finset_1 @ ( k10_xtuple_0 @ A ) ) ) ),file(finset_1,fc36_finset_1)).
thf(rc1_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc1_finset_1)).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
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(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc3_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ),file(finset_1,rc3_finset_1)).
thf(rc3_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc3_funct_1)).
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(rc4_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc4_funct_1)).
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(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(rc9_finset_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finset_1 @ A ) ) ),file(finset_1,rc9_finset_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
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_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_85__orders_1,axiom,( v1_relat_1 @ c1_85__orders_1 ),file(orders_1,c1_85__orders_1)).
thf(dt_c1_85_6_1__orders_1,axiom,( v3_ordinal1 @ c1_85_6_1__orders_1 ),file(orders_1,c1_85_6_1__orders_1)).
thf(dt_c4_85__orders_1,axiom,( ~ ( v1_xboole_0 @ c4_85__orders_1 ) ),file(orders_1,c4_85__orders_1)).
thf(dt_c7_85__orders_1,axiom,( ( v1_relat_1 @ c7_85__orders_1 ) & ( v1_funct_1 @ c7_85__orders_1 ) ),file(orders_1,c7_85__orders_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_orders_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_wellord1 @ A ) & ( v1_orders_1 @ A ) & ( v2_orders_1 @ A ) & ( v3_orders_1 @ A ) ) ) ),file(orders_1,cc1_orders_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc1_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_relat_1 @ A ) ) ),file(relat_1,cc1_relat_1)).
thf(cc1_relat_2,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_relat_2 @ A ) & ( v2_relat_2 @ A ) & ( v3_relat_2 @ A ) & ( v4_relat_2 @ A ) & ( v5_relat_2 @ A ) & ( v6_relat_2 @ A ) & ( v7_relat_2 @ A ) & ( v8_relat_2 @ A ) ) ) ),file(relat_2,cc1_relat_2)).
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_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc3_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v3_relat_1 @ A ) ) ) ),file(relat_1,cc3_relat_1)).
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(cc4_relat_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ) ),file(relat_1,cc4_relat_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_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_finset_1,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v2_finset_1 @ A ) ) ) ),file(finset_1,cc9_finset_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc10_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc10_relat_1)).
thf(fc11_relat_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc11_relat_1)).
thf(fc16_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ B ) ) => ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) ) & ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(relat_1,fc16_relat_1)).
thf(fc17_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) ) & ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(relat_1,fc17_relat_1)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
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(fc4_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(xtuple_0,fc4_xtuple_0)).
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(fc5_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(xtuple_0,fc5_xtuple_0)).
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(fc8_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k9_xtuple_0 @ A ) ) ) ),file(relat_1,fc8_relat_1)).
thf(fc9_relat_1,axiom,( ! [A: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) => ~ ( v1_xboole_0 @ ( k10_xtuple_0 @ A ) ) ) ),file(relat_1,fc9_relat_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(rc1_relat_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) ) ),file(relat_1,rc1_relat_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(rd4_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ( = @ ( k5_relat_1 @ A @ ( k9_xtuple_0 @ A ) ) @ A ) ) ),file(relat_1,rd4_relat_1)).
thf(rd5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( = @ ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ B ) @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,rd5_relat_1)).
thf(e3_85_6_1__orders_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ c1_85_6_1__orders_1 ) & ? [D: $i] : ( ( v3_ordinal1 @ D ) & ( = @ A @ D ) & ? [E: $i] : ( ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) & ( v5_ordinal1 @ E ) & ( = @ B @ ( k1_funct_1 @ c7_85__orders_1 @ ( replSep1 @ ^ [F: $i] : ( m1_subset_1 @ F @ c4_85__orders_1 ) @ ^ [F: $i] : F @ ^ [F: $i] : ! [G: $i] : ( ( r2_hidden @ G @ ( k10_xtuple_0 @ E ) ) => ( ~ ( = @ G @ F ) & ( r2_hidden @ ( k4_tarski @ G @ F ) @ c1_85__orders_1 ) ) ) ) ) ) & ( = @ ( k9_xtuple_0 @ E ) @ D ) & ! [F: $i] : ( ( v3_ordinal1 @ F ) => ! [G: $i] : ( ( ( v1_relat_1 @ G ) & ( v1_funct_1 @ G ) & ( v5_ordinal1 @ G ) ) => ( ( ( r2_hidden @ F @ D ) & ( = @ G @ ( k5_relat_1 @ E @ F ) ) ) => ( = @ ( k1_funct_1 @ E @ F ) @ ( k1_funct_1 @ c7_85__orders_1 @ ( replSep1 @ ^ [H: $i] : ( m1_subset_1 @ H @ c4_85__orders_1 ) @ ^ [H: $i] : H @ ^ [H: $i] : ! [I: $i] : ( ( r2_hidden @ I @ ( k10_xtuple_0 @ G ) ) => ( ~ ( = @ I @ H ) & ( r2_hidden @ ( k4_tarski @ I @ H ) @ c1_85__orders_1 ) ) ) ) ) ) ) ) ) ) ) & ? [D: $i] : ( ( v3_ordinal1 @ D ) & ( = @ A @ D ) & ? [E: $i] : ( ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) & ( v5_ordinal1 @ E ) & ( = @ C @ ( k1_funct_1 @ c7_85__orders_1 @ ( replSep1 @ ^ [F: $i] : ( m1_subset_1 @ F @ c4_85__orders_1 ) @ ^ [F: $i] : F @ ^ [F: $i] : ! [G: $i] : ( ( r2_hidden @ G @ ( k10_xtuple_0 @ E ) ) => ( ~ ( = @ G @ F ) & ( r2_hidden @ ( k4_tarski @ G @ F ) @ c1_85__orders_1 ) ) ) ) ) ) & ( = @ ( k9_xtuple_0 @ E ) @ D ) & ! [F: $i] : ( ( v3_ordinal1 @ F ) => ! [G: $i] : ( ( ( v1_relat_1 @ G ) & ( v1_funct_1 @ G ) & ( v5_ordinal1 @ G ) ) => ( ( ( r2_hidden @ F @ D ) & ( = @ G @ ( k5_relat_1 @ E @ F ) ) ) => ( = @ ( k1_funct_1 @ E @ F ) @ ( k1_funct_1 @ c7_85__orders_1 @ ( replSep1 @ ^ [H: $i] : ( m1_subset_1 @ H @ c4_85__orders_1 ) @ ^ [H: $i] : H @ ^ [H: $i] : ! [I: $i] : ( ( r2_hidden @ I @ ( k10_xtuple_0 @ G ) ) => ( ~ ( = @ I @ H ) & ( r2_hidden @ ( k4_tarski @ I @ H ) @ c1_85__orders_1 ) ) ) ) ) ) ) ) ) ) ) ) => ( = @ B @ C ) ) ),file(orders_1,e3_85_6_1__orders_1)).
thf(e2_85_6_1__orders_1,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ c1_85_6_1__orders_1 ) & ! [B: $i] : ~ ( ? [C: $i] : ( ( v3_ordinal1 @ C ) & ( = @ A @ C ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v5_ordinal1 @ D ) & ( = @ B @ ( k1_funct_1 @ c7_85__orders_1 @ ( replSep1 @ ^ [E: $i] : ( m1_subset_1 @ E @ c4_85__orders_1 ) @ ^ [E: $i] : E @ ^ [E: $i] : ! [F: $i] : ( ( r2_hidden @ F @ ( k10_xtuple_0 @ D ) ) => ( ~ ( = @ F @ E ) & ( r2_hidden @ ( k4_tarski @ F @ E ) @ c1_85__orders_1 ) ) ) ) ) ) & ( = @ ( k9_xtuple_0 @ D ) @ C ) & ! [E: $i] : ( ( v3_ordinal1 @ E ) => ! [F: $i] : ( ( ( v1_relat_1 @ F ) & ( v1_funct_1 @ F ) & ( v5_ordinal1 @ F ) ) => ( ( ( r2_hidden @ E @ C ) & ( = @ F @ ( k5_relat_1 @ D @ E ) ) ) => ( = @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ c7_85__orders_1 @ ( replSep1 @ ^ [G: $i] : ( m1_subset_1 @ G @ c4_85__orders_1 ) @ ^ [G: $i] : G @ ^ [G: $i] : ! [H: $i] : ( ( r2_hidden @ H @ ( k10_xtuple_0 @ F ) ) => ( ~ ( = @ H @ G ) & ( r2_hidden @ ( k4_tarski @ H @ G ) @ c1_85__orders_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),file(orders_1,e2_85_6_1__orders_1)).
thf(s2_funct_1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ( ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( r2_hidden @ C @ B ) & ( A @ C @ D ) & ( A @ C @ E ) ) => ( = @ D @ E ) ) & ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(funct_1,s2_funct_1)).
thf(e4_85_6_1__orders_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ c1_85_6_1__orders_1 ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_85_6_1__orders_1 ) => ? [C: $i] : ( ( v3_ordinal1 @ C ) & ( = @ B @ C ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v5_ordinal1 @ D ) & ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ c7_85__orders_1 @ ( replSep1 @ ^ [E: $i] : ( m1_subset_1 @ E @ c4_85__orders_1 ) @ ^ [E: $i] : E @ ^ [E: $i] : ! [F: $i] : ( ( r2_hidden @ F @ ( k10_xtuple_0 @ D ) ) => ( ~ ( = @ F @ E ) & ( r2_hidden @ ( k4_tarski @ F @ E ) @ c1_85__orders_1 ) ) ) ) ) ) & ( = @ ( k9_xtuple_0 @ D ) @ C ) & ! [E: $i] : ( ( v3_ordinal1 @ E ) => ! [F: $i] : ( ( ( v1_relat_1 @ F ) & ( v1_funct_1 @ F ) & ( v5_ordinal1 @ F ) ) => ( ( ( r2_hidden @ E @ C ) & ( = @ F @ ( k5_relat_1 @ D @ E ) ) ) => ( = @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ c7_85__orders_1 @ ( replSep1 @ ^ [G: $i] : ( m1_subset_1 @ G @ c4_85__orders_1 ) @ ^ [G: $i] : G @ ^ [G: $i] : ! [H: $i] : ( ( r2_hidden @ H @ ( k10_xtuple_0 @ F ) ) => ( ~ ( = @ H @ G ) & ( r2_hidden @ ( k4_tarski @ H @ G ) @ c1_85__orders_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),file(orders_1,e4_85_6_1__orders_1)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
