% Mizar problem: e4_22_1,scheme1,2074,52 
include('Axioms/SET010^0.ax').
thf(c1_22_1_type,type,( c1_22_1__scheme1: $i )).
thf(f4_s18_scheme1_type,type,( f4_s18_scheme1: $i > $i > $i )).
thf(f5_s18_scheme1_type,type,( f5_s18_scheme1: $i > $i > $i )).
thf(f6_s18_scheme1_type,type,( f6_s18_scheme1: $i > $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(p1_s18_scheme1_type,type,( p1_s18_scheme1: $i > $i > $o )).
thf(p2_s18_scheme1_type,type,( p2_s18_scheme1: $i > $i > $o )).
thf(p3_s18_scheme1_type,type,( p3_s18_scheme1: $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(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_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_22_1__scheme1,axiom,( $true ),file(scheme1,c1_22_1__scheme1)).
thf(dt_f4_s18_scheme1,axiom,( $true ),file(scheme1,f4_s18_scheme1)).
thf(dt_f5_s18_scheme1,axiom,( $true ),file(scheme1,f5_s18_scheme1)).
thf(dt_f6_s18_scheme1,axiom,( $true ),file(scheme1,f6_s18_scheme1)).
thf(e3_22_1__scheme1,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ c1_22_1__scheme1 ) & ! [B: $i] : ~ ( ! [C: $i] : ! [D: $i] : ( ( = @ A @ ( k4_tarski @ C @ D ) ) => ( ( ( p1_s18_scheme1 @ C @ D ) => ( = @ B @ ( f4_s18_scheme1 @ C @ D ) ) ) & ( ( p2_s18_scheme1 @ C @ D ) => ( = @ B @ ( f5_s18_scheme1 @ C @ D ) ) ) & ( ( p3_s18_scheme1 @ C @ D ) => ( = @ B @ ( f6_s18_scheme1 @ C @ D ) ) ) ) ) ) ) ),file(scheme1,e3_22_1__scheme1)).
thf(s1_classes1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(classes1,s1_classes1)).
thf(e4_22_1__scheme1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ c1_22_1__scheme1 ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_22_1__scheme1 ) => ! [C: $i] : ! [D: $i] : ( ( = @ B @ ( k4_tarski @ C @ D ) ) => ( ( ( p1_s18_scheme1 @ C @ D ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( f4_s18_scheme1 @ C @ D ) ) ) & ( ( p2_s18_scheme1 @ C @ D ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( f5_s18_scheme1 @ C @ D ) ) ) & ( ( p3_s18_scheme1 @ C @ D ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( f6_s18_scheme1 @ C @ D ) ) ) ) ) ) ) ),file(scheme1,e4_22_1__scheme1)).
