% Mizar problem: e1_4_1_2,enumset1,99,58 
include('Axioms/SET010^0.ax').
thf(c1_4_type,type,( c1_4__enumset1: $i )).
thf(c2_4_type,type,( c2_4__enumset1: $i )).
thf(c3_4_type,type,( c3_4__enumset1: $i )).
thf(c4_4_type,type,( c4_4__enumset1: $i )).
thf(c5_4_type,type,( c5_4__enumset1: $i )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_c1_4__enumset1,axiom,( $true ),file(enumset1,c1_4__enumset1)).
thf(dt_c2_4__enumset1,axiom,( $true ),file(enumset1,c2_4__enumset1)).
thf(dt_c3_4__enumset1,axiom,( $true ),file(enumset1,c3_4__enumset1)).
thf(dt_c4_4__enumset1,axiom,( $true ),file(enumset1,c4_4__enumset1)).
thf(dt_c5_4__enumset1,axiom,( $true ),file(enumset1,c5_4__enumset1)).
thf(s3_xboole_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ! [D: $i] : ( ( r2_hidden @ D @ B ) <=> ( A @ D ) ) & ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( A @ D ) ) ) => ( = @ B @ C ) ) ),file(xboole_0,s3_xboole_0)).
thf(e1_4_1_2__enumset1,conjecture,( ! [A: $i] : ! [B: $i] : ( ( ! [C: $i] : ( ( r2_hidden @ C @ A ) <=> ~ ( ~ ( = @ C @ c1_4__enumset1 ) & ~ ( = @ C @ c2_4__enumset1 ) & ~ ( = @ C @ c3_4__enumset1 ) & ~ ( = @ C @ c4_4__enumset1 ) & ~ ( = @ C @ c5_4__enumset1 ) ) ) & ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ~ ( ~ ( = @ C @ c1_4__enumset1 ) & ~ ( = @ C @ c2_4__enumset1 ) & ~ ( = @ C @ c3_4__enumset1 ) & ~ ( = @ C @ c4_4__enumset1 ) & ~ ( = @ C @ c5_4__enumset1 ) ) ) ) => ( = @ A @ B ) ) ),file(enumset1,e1_4_1_2__enumset1)).
