% Mizar problem: e7_79_1_1_2,classes1,2063,42 
include('Axioms/SET010^0.ax').
thf(c2_79_1_1_2_type,type,( c2_79_1_1_2__classes1: $i )).
thf(f1_s1_classes1_type,type,( f1_s1_classes1: $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(k3_ordinal2_type,type,( k3_ordinal2: $i > $i )).
thf(k4_classes1_type,type,( k4_classes1: $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(p1_s1_classes1_type,type,( p1_s1_classes1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
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(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_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(fc2_classes1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( v1_ordinal1 @ ( k4_classes1 @ A ) ) ) ),file(classes1,fc2_classes1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
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_k3_ordinal2,axiom,( ! [A: $i] : ( v3_ordinal1 @ ( k3_ordinal2 @ A ) ) ),file(ordinal2,k3_ordinal2)).
thf(dt_k4_classes1,axiom,( $true ),file(classes1,k4_classes1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c2_79_1_1_2__classes1,axiom,( ( v1_relat_1 @ c2_79_1_1_2__classes1 ) & ( v1_funct_1 @ c2_79_1_1_2__classes1 ) ),file(classes1,c2_79_1_1_2__classes1)).
thf(dt_f1_s1_classes1,axiom,( $true ),file(classes1,f1_s1_classes1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e6_79_1_1_2__classes1,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ f1_s1_classes1 ) & ! [B: $i] : ~ ( ( r2_hidden @ B @ ( k4_classes1 @ ( k3_ordinal2 @ ( k10_xtuple_0 @ c2_79_1_1_2__classes1 ) ) ) ) & ( p1_s1_classes1 @ A @ B ) ) ) ),file(classes1,e6_79_1_1_2__classes1)).
thf(s5_funct_1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ! [C: $i] : ( ! [D: $i] : ~ ( ( r2_hidden @ D @ C ) & ! [E: $i] : ~ ( ( r2_hidden @ E @ B ) & ( A @ D @ E ) ) ) => ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ ( k9_xtuple_0 @ D ) @ C ) & ( r1_tarski @ ( k10_xtuple_0 @ D ) @ B ) & ! [E: $i] : ( ( r2_hidden @ E @ C ) => ( A @ E @ ( k1_funct_1 @ D @ E ) ) ) ) ) ),file(funct_1,s5_funct_1)).
thf(e7_79_1_1_2__classes1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ f1_s1_classes1 ) & ( r1_tarski @ ( k10_xtuple_0 @ A ) @ ( k4_classes1 @ ( k3_ordinal2 @ ( k10_xtuple_0 @ c2_79_1_1_2__classes1 ) ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ f1_s1_classes1 ) => ( p1_s1_classes1 @ B @ ( k1_funct_1 @ A @ B ) ) ) ) ),file(classes1,e7_79_1_1_2__classes1)).
