% Mizar problem: e5_21_2,card_3,492,66 
include('Axioms/SET010^0.ax').
thf(c1_21_type,type,( c1_21__card_3: $i )).
thf(c2_21_2_type,type,( c2_21_2__card_3: $i )).
thf(c3_21_2_type,type,( c3_21_2__card_3: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $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_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_21__card_3,axiom,( $true ),file(card_3,c1_21__card_3)).
thf(dt_c2_21_2__card_3,axiom,( ( v1_relat_1 @ c2_21_2__card_3 ) & ( v1_funct_1 @ c2_21_2__card_3 ) ),file(card_3,c2_21_2__card_3)).
thf(dt_c3_21_2__card_3,axiom,( $true ),file(card_3,c3_21_2__card_3)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s1_partfun1,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] : ( ( r2_hidden @ F @ D ) => ( ( ( C @ F ) => ( = @ ( k1_funct_1 @ E @ F ) @ ( B @ F ) ) ) & ( ~ ( C @ F ) => ( = @ ( k1_funct_1 @ E @ F ) @ ( A @ F ) ) ) ) ) ) ),file(partfun1,s1_partfun1)).
thf(e5_21_2__card_3,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k9_xtuple_0 @ c2_21_2__card_3 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c2_21_2__card_3 ) ) => ( ( ( = @ c1_21__card_3 @ B ) => ( = @ ( k1_funct_1 @ A @ B ) @ c3_21_2__card_3 ) ) & ( ~ ( = @ c1_21__card_3 @ B ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ c2_21_2__card_3 @ B ) ) ) ) ) ) ),file(card_3,e5_21_2__card_3)).
