% Mizar problem: e1_5_2_1,twoscomp,239,52 
include('Axioms/SET010^0.ax').
thf(n2_type,type,( np__2: $i )).
thf(k10_finseq_1_type,type,( k10_finseq_1: $i > $i > $i )).
thf(k1_binarith_type,type,( k1_binarith: $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_numbers_type,type,( k1_numbers: $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k3_xboolean_type,type,( k3_xboolean: $i > $i )).
thf(k4_finseq_2_type,type,( k4_finseq_2: $i > $i > $i )).
thf(k4_ordinal1_type,type,( k4_ordinal1: $i )).
thf(k5_numbers_type,type,( k5_numbers: $i )).
thf(k5_xboolean_type,type,( k5_xboolean: $i > $i > $i )).
thf(k6_margrel1_type,type,( k6_margrel1: $i )).
thf(k9_margrel1_type,type,( k9_margrel1: $i > $i )).
thf(m1_finseq_2_type,type,( m1_finseq_2: $i > $i > $o )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(m2_subset_1_type,type,( m2_subset_1: $i > $i > $i > $o )).
thf(v1_card_3_type,type,( v1_card_3: $i > $o )).
thf(v1_facirc_1_type,type,( v1_facirc_1: $i > $o )).
thf(v1_finseq_1_type,type,( v1_finseq_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_funct_2_type,type,( v1_funct_2: $i > $i > $i > $o )).
thf(v1_margrel1_type,type,( v1_margrel1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $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_xboolean_type,type,( v1_xboolean: $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_card_3_type,type,( v2_card_3: $i > $o )).
thf(v2_facirc_1_type,type,( v2_facirc_1: $i > $o )).
thf(v2_finseq_1_type,type,( v2_finseq_1: $i > $o )).
thf(v2_funct_1_type,type,( v2_funct_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v2_xxreal_0_type,type,( v2_xxreal_0: $i > $o )).
thf(v3_card_1_type,type,( v3_card_1: $i > $i > $o )).
thf(v3_finseq_1_type,type,( v3_finseq_1: $i > $o )).
thf(v3_funct_1_type,type,( v3_funct_1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v4_card_3_type,type,( v4_card_3: $i > $o )).
thf(v4_funct_1_type,type,( v4_funct_1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(v5_card_3_type,type,( v5_card_3: $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(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
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_3,axiom,( ! [A: $i] : ( ( ~ ( v1_finset_1 @ A ) & ( v4_card_3 @ A ) ) => ( v5_card_3 @ A ) ) ),file(card_3,cc5_card_3)).
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(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(rc2_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) & ( v3_ordinal1 @ A ) ) ),file(ordinal1,rc2_ordinal1)).
thf(rc3_facirc_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v1_funct_1 @ B ) & ( v2_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v3_card_1 @ B @ A ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) & ( v4_card_3 @ B ) & ( v2_facirc_1 @ B ) ) ) ),file(facirc_1,rc3_facirc_1)).
thf(rc4_facirc_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v2_funct_1 @ A ) & ( v1_finset_1 @ A ) & ( v1_finseq_1 @ A ) & ( v2_finseq_1 @ A ) & ( v4_card_3 @ A ) & ( v2_facirc_1 @ A ) ) ),file(facirc_1,rc4_facirc_1)).
thf(rc5_card_3,axiom,( ? [A: $i] : ( v5_card_3 @ A ) ),file(card_3,rc5_card_3)).
thf(dt_k4_ordinal1,axiom,( $true ),file(ordinal1,k4_ordinal1)).
thf(cc10_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v1_finseq_1 @ B ) ) ) ),file(finseq_1,cc10_finseq_1)).
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(cc11_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v3_finseq_1 @ B ) ) ) ),file(finseq_1,cc11_finseq_1)).
thf(cc1_facirc_1,axiom,( ! [A: $i] : ( ( v1_xtuple_0 @ A ) => ~ ( v1_xboole_0 @ A ) ) ),file(facirc_1,cc1_facirc_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc4_facirc_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ~ ( v1_facirc_1 @ A ) ) => ( v1_xboole_0 @ A ) ) ),file(facirc_1,cc4_facirc_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_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ A ) => ( v3_ordinal1 @ B ) ) ) ),file(ordinal1,cc5_ordinal1)).
thf(cc6_card_3,axiom,( ! [A: $i] : ( ( v1_finset_1 @ A ) => ( v4_card_3 @ A ) ) ),file(card_3,cc6_card_3)).
thf(cc7_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ) ),file(finseq_1,cc7_finseq_1)).
thf(cc8_card_3,axiom,( ! [A: $i] : ( ( v2_card_3 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v2_card_3 @ B ) ) ) ),file(card_3,cc8_card_3)).
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_ordinal1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k4_ordinal1 ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc8_ordinal1)).
thf(cc9_finseq_1,axiom,( ! [A: $i] : ( ( v3_finseq_1 @ A ) => ( v4_funct_1 @ A ) ) ),file(finseq_1,cc9_finseq_1)).
thf(cc9_funct_1,axiom,( ! [A: $i] : ( ( v4_funct_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v4_funct_1 @ B ) ) ) ),file(funct_1,cc9_funct_1)).
thf(fc10_card_3,axiom,( v5_card_3 @ k4_ordinal1 ),file(card_3,fc10_card_3)).
thf(fc12_facirc_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xtuple_0 @ A ) & ~ ( v1_xtuple_0 @ B ) ) => ( v2_facirc_1 @ ( k10_finseq_1 @ A @ B ) ) ) ),file(facirc_1,fc12_facirc_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(fc29_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v3_finseq_1 @ A ) & ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) => ( v1_finseq_1 @ ( k1_funct_1 @ B @ C ) ) ) ),file(finseq_1,fc29_finseq_1)).
thf(fc6_ordinal1,axiom,( ~ ( v1_xboole_0 @ k4_ordinal1 ) & ( v3_ordinal1 @ k4_ordinal1 ) ),file(ordinal1,fc6_ordinal1)).
thf(rc1_card_3,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_card_3 @ A ) ) ),file(card_3,rc1_card_3)).
thf(rc1_facirc_1,axiom,( ? [A: $i] : ~ ( v1_xtuple_0 @ A ) ),file(facirc_1,rc1_facirc_1)).
thf(rc1_margrel1,axiom,( ? [A: $i] : ( ( v3_finseq_1 @ A ) & ( v2_card_3 @ A ) ) ),file(margrel1,rc1_margrel1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(rc2_facirc_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_facirc_1 @ A ) ) ),file(facirc_1,rc2_facirc_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(rc3_card_3,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) & ( v2_card_3 @ A ) ) ),file(card_3,rc3_card_3)).
thf(rc3_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc3_finseq_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_finseq_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ~ ( v1_xboole_0 @ A ) & ( v1_finset_1 @ A ) & ( v1_finseq_1 @ A ) & ( v2_finseq_1 @ A ) ) ),file(finseq_1,rc4_finseq_1)).
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(rc6_card_3,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ~ ( v1_finset_1 @ A ) ) ),file(card_3,rc6_card_3)).
thf(rc7_finseq_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v3_card_1 @ B @ A ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ) ),file(finseq_1,rc7_finseq_1)).
thf(rc7_funct_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v4_funct_1 @ A ) ) ),file(funct_1,rc7_funct_1)).
thf(rc8_finseq_1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v3_finseq_1 @ A ) ) ),file(finseq_1,rc8_finseq_1)).
thf(rc9_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_finset_1 @ B ) & ( v1_finseq_1 @ B ) & ( v2_finseq_1 @ B ) ) ),file(finseq_1,rc9_finseq_1)).
thf(involutiveness_k3_xboolean,axiom,( ! [A: $i] : ( ( v1_xboolean @ A ) => ( = @ ( k3_xboolean @ ( k3_xboolean @ A ) ) @ A ) ) ),file(xboolean,k3_xboolean)).
thf(commutativity_k5_xboolean,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xboolean @ A ) & ( v1_xboolean @ B ) ) => ( = @ ( k5_xboolean @ A @ B ) @ ( k5_xboolean @ B @ A ) ) ) ),file(xboolean,k5_xboolean)).
thf(idempotence_k5_xboolean,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xboolean @ A ) & ( v1_xboolean @ B ) ) => ( = @ ( k5_xboolean @ A @ A ) @ A ) ) ),file(xboolean,k5_xboolean)).
thf(redefinition_k5_numbers,axiom,( = @ k5_numbers @ k4_ordinal1 ),file(numbers,k5_numbers)).
thf(redefinition_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) <=> ( m1_subset_1 @ C @ B ) ) ) ),file(subset_1,m2_subset_1)).
thf(dt_k1_numbers,axiom,( $true ),file(numbers,k1_numbers)).
thf(dt_k3_xboolean,axiom,( ! [A: $i] : ( ( v1_xboolean @ A ) => ( v1_xboolean @ ( k3_xboolean @ A ) ) ) ),file(xboolean,k3_xboolean)).
thf(dt_k5_numbers,axiom,( m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ) ),file(numbers,k5_numbers)).
thf(dt_k5_xboolean,axiom,( $true ),file(xboolean,k5_xboolean)).
thf(dt_m1_finseq_2,axiom,( $true ),file(finseq_2,m1_finseq_2)).
thf(dt_m2_subset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ~ ( v1_xboole_0 @ A ) & ~ ( v1_xboole_0 @ B ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) => ! [C: $i] : ( ( m2_subset_1 @ C @ A @ B ) => ( m1_subset_1 @ C @ A ) ) ) ),file(subset_1,m2_subset_1)).
thf(cc1_card_3,axiom,( ! [A: $i] : ( ( ( v1_xboole_0 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_card_3 @ A ) ) ) ),file(card_3,cc1_card_3)).
thf(cc1_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc1_finseq_1)).
thf(cc1_funct_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v1_funct_1 @ A ) ) ),file(funct_1,cc1_funct_1)).
thf(cc1_margrel1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v2_card_3 @ A ) ) ),file(margrel1,cc1_margrel1)).
thf(cc1_xboolean,axiom,( ! [A: $i] : ( ( v1_xboolean @ A ) => ( v7_ordinal1 @ A ) ) ),file(xboolean,cc1_xboolean)).
thf(cc2_facirc_1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( ( v7_ordinal1 @ A ) & ~ ( v1_xtuple_0 @ A ) ) ) ),file(facirc_1,cc2_facirc_1)).
thf(cc2_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finset_1 @ A ) ) ) ),file(finseq_1,cc2_finseq_1)).
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_facirc_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ~ ( v1_facirc_1 @ A ) ) ),file(facirc_1,cc3_facirc_1)).
thf(cc3_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_funct_1 @ B ) ) ) ),file(funct_1,cc3_funct_1)).
thf(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc3_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc3_relset_1)).
thf(cc4_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc4_finseq_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_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_xboole_0 @ A ) => ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) ) => ( v1_xboole_0 @ C ) ) ) ),file(relset_1,cc4_relset_1)).
thf(cc5_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ k5_numbers ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) ) ),file(finseq_1,cc5_finseq_1)).
thf(cc6_finseq_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_finseq_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_finseq_1 @ A ) ) ) ),file(finseq_1,cc6_finseq_1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_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(cc8_finseq_1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_finseq_1 @ A ) ) ),file(finseq_1,cc8_finseq_1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(fc4_margrel1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_margrel1 @ A ) ) => ( v1_xboolean @ ( k1_funct_1 @ A @ B ) ) ) ),file(margrel1,fc4_margrel1)).
thf(fc4_xboolean,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xboolean @ A ) & ( v1_xboolean @ B ) ) => ( v1_xboolean @ ( k5_xboolean @ A @ B ) ) ) ),file(xboolean,fc4_xboolean)).
thf(rc1_finseq_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ k5_numbers @ A ) ) ) & ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ k5_numbers ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_finseq_1 @ B ) ) ),file(finseq_1,rc1_finseq_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) & ( v1_xboole_0 @ C ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ),file(relset_1,rc1_relset_1)).
thf(rc1_xboolean,axiom,( ? [A: $i] : ( v1_xboolean @ A ) ),file(xboolean,rc1_xboolean)).
thf(rc2_margrel1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_margrel1 @ A ) ) ),file(margrel1,rc2_margrel1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(rc6_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) ) ),file(funct_1,rc6_funct_1)).
thf(commutativity_k1_binarith,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k6_margrel1 ) & ( m1_subset_1 @ B @ k6_margrel1 ) ) => ( = @ ( k1_binarith @ A @ B ) @ ( k1_binarith @ B @ A ) ) ) ),file(binarith,k1_binarith)).
thf(idempotence_k1_binarith,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k6_margrel1 ) & ( m1_subset_1 @ B @ k6_margrel1 ) ) => ( = @ ( k1_binarith @ A @ A ) @ A ) ) ),file(binarith,k1_binarith)).
thf(involutiveness_k9_margrel1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k6_margrel1 ) => ( = @ ( k9_margrel1 @ ( k9_margrel1 @ A ) ) @ A ) ) ),file(margrel1,k9_margrel1)).
thf(redefinition_k1_binarith,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k6_margrel1 ) & ( m1_subset_1 @ B @ k6_margrel1 ) ) => ( = @ ( k1_binarith @ A @ B ) @ ( k5_xboolean @ A @ B ) ) ) ),file(binarith,k1_binarith)).
thf(redefinition_k9_margrel1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k6_margrel1 ) => ( = @ ( k9_margrel1 @ A ) @ ( k3_xboolean @ A ) ) ) ),file(margrel1,k9_margrel1)).
thf(dt_k10_finseq_1,axiom,( $true ),file(finseq_1,k10_finseq_1)).
thf(dt_k1_binarith,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( m1_subset_1 @ A @ k6_margrel1 ) & ( m1_subset_1 @ B @ k6_margrel1 ) ) => ( m1_subset_1 @ ( k1_binarith @ A @ B ) @ k6_margrel1 ) ) ),file(binarith,k1_binarith)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k4_finseq_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( v7_ordinal1 @ A ) => ( m1_finseq_2 @ ( k4_finseq_2 @ A @ B ) @ B ) ) ),file(finseq_2,k4_finseq_2)).
thf(dt_k6_margrel1,axiom,( $true ),file(margrel1,k6_margrel1)).
thf(dt_k9_margrel1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k6_margrel1 ) => ( m1_subset_1 @ ( k9_margrel1 @ A ) @ k6_margrel1 ) ) ),file(margrel1,k9_margrel1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc2_margrel1,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ k6_margrel1 ) => ( v1_xboolean @ A ) ) ),file(margrel1,cc2_margrel1)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(cc3_margrel1,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ k6_margrel1 ) ) ) => ( ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ A @ k6_margrel1 ) ) => ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ A @ k6_margrel1 ) & ( v1_margrel1 @ B ) ) ) ) ),file(margrel1,cc3_margrel1)).
thf(fc10_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_finseq_1 @ ( k10_finseq_1 @ A @ B ) ) ),file(finseq_1,fc10_finseq_1)).
thf(fc19_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ~ ( v1_xboole_0 @ ( k10_finseq_1 @ A @ B ) ) ),file(finseq_1,fc19_finseq_1)).
thf(fc25_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( v3_card_1 @ ( k10_finseq_1 @ A @ B ) @ np__2 ) ),file(finseq_1,fc25_finseq_1)).
thf(fc2_margrel1,axiom,( ~ ( v1_xboole_0 @ k6_margrel1 ) ),file(margrel1,fc2_margrel1)).
thf(fc8_finseq_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ ( k10_finseq_1 @ A @ B ) ) & ( v1_funct_1 @ ( k10_finseq_1 @ A @ B ) ) ) ),file(finseq_1,fc8_finseq_1)).
thf(spc2_numerals,axiom,( ( v2_xxreal_0 @ np__2 ) & ( m2_subset_1 @ np__2 @ k1_numbers @ k5_numbers ) & ( m1_subset_1 @ np__2 @ k5_numbers ) & ( m1_subset_1 @ np__2 @ k1_numbers ) ),file(numerals,spc2_numerals)).
thf(spc2_boole,axiom,( ~ ( v1_xboole_0 @ np__2 ) ),file(boole,spc2_boole)).
thf(s1_facirc_1,axiom,( ! [A: $i > $i > $i] : ? [B: $i] : ( ( v1_funct_1 @ B ) & ( v1_funct_2 @ B @ ( k4_finseq_2 @ np__2 @ k6_margrel1 ) @ k6_margrel1 ) & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k4_finseq_2 @ np__2 @ k6_margrel1 ) @ k6_margrel1 ) ) ) & ! [C: $i] : ( ( m1_subset_1 @ C @ k6_margrel1 ) => ! [D: $i] : ( ( m1_subset_1 @ D @ k6_margrel1 ) => ( = @ ( k1_funct_1 @ B @ ( k10_finseq_1 @ C @ D ) ) @ ( A @ C @ D ) ) ) ) ) ),file(facirc_1,s1_facirc_1)).
thf(e1_5_2_1__twoscomp,conjecture,( ? [A: $i] : ( ( v1_funct_1 @ A ) & ( v1_funct_2 @ A @ ( k4_finseq_2 @ np__2 @ k6_margrel1 ) @ k6_margrel1 ) & ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k4_finseq_2 @ np__2 @ k6_margrel1 ) @ k6_margrel1 ) ) ) & ! [B: $i] : ( ( m1_subset_1 @ B @ k6_margrel1 ) => ! [C: $i] : ( ( m1_subset_1 @ C @ k6_margrel1 ) => ( = @ ( k1_funct_1 @ A @ ( k10_finseq_1 @ B @ C ) ) @ ( k9_margrel1 @ ( k1_binarith @ ( k9_margrel1 @ B ) @ C ) ) ) ) ) ) ),file(twoscomp,e1_5_2_1__twoscomp)).
