% Mizar problem: e8_7,finset_1,127,64 
include('Axioms/SET010^0.ax').
thf(c3_7_type,type,( c3_7__finset_1: $i )).
thf(c4_7_type,type,( c4_7__finset_1: $i )).
thf(c5_7_type,type,( c5_7__finset_1: $i )).
thf(c6_7_type,type,( c6_7__finset_1: $i )).
thf(k10_ordinal2_type,type,( k10_ordinal2: $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k5_ordinal3_type,type,( k5_ordinal3: $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(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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k10_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k10_ordinal2 @ A @ B ) ) ) ),file(ordinal2,k10_ordinal2)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k5_ordinal3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k5_ordinal3 @ A @ B ) ) ) ),file(ordinal3,k5_ordinal3)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c3_7__finset_1,axiom,( ( v1_relat_1 @ c3_7__finset_1 ) & ( v1_funct_1 @ c3_7__finset_1 ) ),file(finset_1,c3_7__finset_1)).
thf(dt_c4_7__finset_1,axiom,( ( v1_relat_1 @ c4_7__finset_1 ) & ( v1_funct_1 @ c4_7__finset_1 ) ),file(finset_1,c4_7__finset_1)).
thf(dt_c5_7__finset_1,axiom,( v3_ordinal1 @ c5_7__finset_1 ),file(finset_1,c5_7__finset_1)).
thf(dt_c6_7__finset_1,axiom,( v3_ordinal1 @ c6_7__finset_1 ),file(finset_1,c6_7__finset_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
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(s1_finset_1,axiom,( ! [A: $i > $i] : ! [B: $i > $i] : ! [C: $i > $o] : ! [D: $i] : ? [E: $i] : ( ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) & ( = @ ( k9_xtuple_0 @ E ) @ D ) & ! [F: $i] : ( ( v3_ordinal1 @ F ) => ( ( r2_hidden @ F @ D ) => ( ( ( C @ F ) => ( = @ ( k1_funct_1 @ E @ F ) @ ( B @ F ) ) ) & ( ~ ( C @ F ) => ( = @ ( k1_funct_1 @ E @ F ) @ ( A @ F ) ) ) ) ) ) ) ),file(finset_1,s1_finset_1)).
thf(e8_7__finset_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k10_ordinal2 @ c5_7__finset_1 @ c6_7__finset_1 ) ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ ( k10_ordinal2 @ c5_7__finset_1 @ c6_7__finset_1 ) ) => ( ( ( r2_hidden @ B @ c5_7__finset_1 ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ c3_7__finset_1 @ B ) ) ) & ( ~ ( r2_hidden @ B @ c5_7__finset_1 ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ c4_7__finset_1 @ ( k5_ordinal3 @ B @ c5_7__finset_1 ) ) ) ) ) ) ) ) ),file(finset_1,e8_7__finset_1)).
