% Mizar problem: e4_80_1_1,ordinal3,1807,18 
include('Axioms/SET010^0.ax').
thf(c1_80_1_1_type,type,( c1_80_1_1__ordinal3: $i )).
thf(c2_80_1_1_type,type,( c2_80_1_1__ordinal3: $i )).
thf(k11_ordinal2_type,type,( k11_ordinal2: $i > $i > $i )).
thf(k1_ordinal1_type,type,( k1_ordinal1: $i > $i )).
thf(k1_xboole_0_type,type,( k1_xboole_0: $i )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_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(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(cc3_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc3_ordinal1)).
thf(cc4_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v5_ordinal1 @ A ) ) ),file(ordinal1,cc4_ordinal1)).
thf(cc7_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v7_ordinal1 @ A ) ) ),file(ordinal1,cc7_ordinal1)).
thf(cc9_ordinal1,axiom,( ! [A: $i] : ( ( v1_xboole_0 @ A ) => ( v6_ordinal1 @ A ) ) ),file(ordinal1,cc9_ordinal1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
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_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_xboole_0)).
thf(rc5_ordinal1,axiom,( ? [A: $i] : ( ~ ( v1_xboole_0 @ A ) & ( v7_ordinal1 @ A ) ) ),file(ordinal1,rc5_ordinal1)).
thf(dt_k11_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k11_ordinal2 @ A @ B ) ) ) ),file(ordinal2,k11_ordinal2)).
thf(dt_k1_ordinal1,axiom,( $true ),file(ordinal1,k1_ordinal1)).
thf(dt_k1_xboole_0,axiom,( $true ),file(xboole_0,k1_xboole_0)).
thf(dt_c1_80_1_1__ordinal3,axiom,( ( v3_ordinal1 @ c1_80_1_1__ordinal3 ) & ( v7_ordinal1 @ c1_80_1_1__ordinal3 ) ),file(ordinal3,c1_80_1_1__ordinal3)).
thf(dt_c2_80_1_1__ordinal3,axiom,( ( v3_ordinal1 @ c2_80_1_1__ordinal3 ) & ( v7_ordinal1 @ c2_80_1_1__ordinal3 ) ),file(ordinal3,c2_80_1_1__ordinal3)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(cc6_ordinal1,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc6_ordinal1)).
thf(fc1_ordinal1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_ordinal1 @ A ) ) ),file(ordinal1,fc1_ordinal1)).
thf(fc1_xboole_0,axiom,( v1_xboole_0 @ k1_xboole_0 ),file(xboole_0,fc1_xboole_0)).
thf(fc2_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ~ ( v1_xboole_0 @ ( k1_ordinal1 @ A ) ) & ( v3_ordinal1 @ ( k1_ordinal1 @ A ) ) ) ) ),file(ordinal1,fc2_ordinal1)).
thf(fc4_ordinal3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) & ( v3_ordinal1 @ B ) & ( v7_ordinal1 @ B ) ) => ( ( v3_ordinal1 @ ( k11_ordinal2 @ A @ B ) ) & ( v7_ordinal1 @ ( k11_ordinal2 @ A @ B ) ) ) ) ),file(ordinal3,fc4_ordinal3)).
thf(fc7_ordinal1,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) => ( v7_ordinal1 @ ( k1_ordinal1 @ A ) ) ) ),file(ordinal1,fc7_ordinal1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc4_ordinal1,axiom,( ? [A: $i] : ( v7_ordinal1 @ A ) ),file(ordinal1,rc4_ordinal1)).
thf(e3_80_1_1__ordinal3,axiom,( = @ ( k11_ordinal2 @ c1_80_1_1__ordinal3 @ k1_xboole_0 ) @ ( k11_ordinal2 @ k1_xboole_0 @ c1_80_1_1__ordinal3 ) ),file(ordinal3,e3_80_1_1__ordinal3)).
thf(e1_80_1_1__ordinal3,axiom,( ! [A: $i] : ( ( ( v3_ordinal1 @ A ) & ( v7_ordinal1 @ A ) ) => ( ( = @ ( k11_ordinal2 @ c1_80_1_1__ordinal3 @ A ) @ ( k11_ordinal2 @ A @ c1_80_1_1__ordinal3 ) ) => ( = @ ( k11_ordinal2 @ c1_80_1_1__ordinal3 @ ( k1_ordinal1 @ A ) ) @ ( k11_ordinal2 @ ( k1_ordinal1 @ A ) @ c1_80_1_1__ordinal3 ) ) ) ) ),file(ordinal3,e1_80_1_1__ordinal3)).
thf(s17_ordinal2,axiom,( ! [A: $i] : ! [B: $i > $o] : ( ( ( B @ k1_xboole_0 ) & ! [C: $i] : ( ( v7_ordinal1 @ C ) => ( ( B @ C ) => ( B @ ( k1_ordinal1 @ C ) ) ) ) ) => ( B @ A ) ) ),file(ordinal2,s17_ordinal2)).
thf(e4_80_1_1__ordinal3,conjecture,( = @ ( k11_ordinal2 @ c1_80_1_1__ordinal3 @ c2_80_1_1__ordinal3 ) @ ( k11_ordinal2 @ c2_80_1_1__ordinal3 @ c1_80_1_1__ordinal3 ) ),file(ordinal3,e4_80_1_1__ordinal3)).
