% Mizar problem: e6_56,ordinal1,969,40 
include('Axioms/SET010^0.ax').
thf(c1_56_type,type,( c1_56__ordinal1: $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(v1_funct_1_type,type,( v1_funct_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_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_56__ordinal1,axiom,( $true ),file(ordinal1,c1_56__ordinal1)).
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(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e5_56__ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ c1_56__ordinal1 ) & ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v5_ordinal1 @ D ) ) => ( ( = @ D @ A ) => ( = @ ( k9_xtuple_0 @ D ) @ B ) ) ) & ( r2_hidden @ A @ c1_56__ordinal1 ) & ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v5_ordinal1 @ D ) ) => ( ( = @ D @ A ) => ( = @ ( k9_xtuple_0 @ D ) @ C ) ) ) ) => ( = @ B @ C ) ) ),file(ordinal1,e5_56__ordinal1)).
thf(s1_funct_1,axiom,( ! [A: $i] : ! [B: $i > $i > $o] : ( ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( B @ C @ D ) & ( B @ C @ E ) ) => ( = @ D @ E ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ! [D: $i] : ! [E: $i] : ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) <=> ( ( r2_hidden @ D @ A ) & ( B @ D @ E ) ) ) ) ) ),file(funct_1,s1_funct_1)).
thf(e6_56__ordinal1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ! [B: $i] : ! [C: $i] : ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) <=> ( ( r2_hidden @ B @ c1_56__ordinal1 ) & ( r2_hidden @ B @ c1_56__ordinal1 ) & ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( v5_ordinal1 @ D ) ) => ( ( = @ D @ B ) => ( = @ ( k9_xtuple_0 @ D ) @ C ) ) ) ) ) ) ),file(ordinal1,e6_56__ordinal1)).
