% Mizar problem: e3_22_1_1,algspec1,517,53 
include('Axioms/SET010^0.ax').
thf(c1_22_type,type,( c1_22__algspec1: $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(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
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_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_22__algspec1,axiom,( ( v1_relat_1 @ c1_22__algspec1 ) & ( v1_funct_1 @ c1_22__algspec1 ) ),file(algspec1,c1_22__algspec1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e2_22_1_1__algspec1,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ ( k10_xtuple_0 @ c1_22__algspec1 ) ) & ! [B: $i] : ~ ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c1_22__algspec1 ) ) & ( = @ ( k1_funct_1 @ c1_22__algspec1 @ B ) @ A ) ) ) ),file(algspec1,e2_22_1_1__algspec1)).
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(e3_22_1_1__algspec1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k10_xtuple_0 @ c1_22__algspec1 ) ) & ( r1_tarski @ ( k10_xtuple_0 @ A ) @ ( k9_xtuple_0 @ c1_22__algspec1 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k10_xtuple_0 @ c1_22__algspec1 ) ) => ( = @ ( k1_funct_1 @ c1_22__algspec1 @ ( k1_funct_1 @ A @ B ) ) @ B ) ) ) ),file(algspec1,e3_22_1_1__algspec1)).
