% Mizar problem: e9_17_2_1,funct_5,345,52 
include('Axioms/SET010^0.ax').
thf(c1_17_type,type,( c1_17__funct_5: $i )).
thf(c3_17_2_1_type,type,( c3_17_2_1__funct_5: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_xtuple_0_type,type,( k1_xtuple_0: $i > $i )).
thf(k2_xtuple_0_type,type,( k2_xtuple_0: $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_k1_xtuple_0,axiom,( $true ),file(xtuple_0,k1_xtuple_0)).
thf(dt_k2_xtuple_0,axiom,( $true ),file(xtuple_0,k2_xtuple_0)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_17__funct_5,axiom,( ( v1_relat_1 @ c1_17__funct_5 ) & ( v1_funct_1 @ c1_17__funct_5 ) ),file(funct_5,c1_17__funct_5)).
thf(dt_c3_17_2_1__funct_5,axiom,( $true ),file(funct_5,c3_17_2_1__funct_5)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e8_17_2_1__funct_5,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ c3_17_2_1__funct_5 ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ D @ ( k1_funct_1 @ c1_17__funct_5 @ ( k1_xtuple_0 @ A ) ) ) & ( = @ B @ ( k1_funct_1 @ D @ ( k2_xtuple_0 @ A ) ) ) ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ D @ ( k1_funct_1 @ c1_17__funct_5 @ ( k1_xtuple_0 @ A ) ) ) & ( = @ C @ ( k1_funct_1 @ D @ ( k2_xtuple_0 @ A ) ) ) ) ) => ( = @ B @ C ) ) ),file(funct_5,e8_17_2_1__funct_5)).
thf(e7_17_2_1__funct_5,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ c3_17_2_1__funct_5 ) & ! [B: $i] : ~ ( ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ C @ ( k1_funct_1 @ c1_17__funct_5 @ ( k1_xtuple_0 @ A ) ) ) & ( = @ B @ ( k1_funct_1 @ C @ ( k2_xtuple_0 @ A ) ) ) ) ) ) ),file(funct_5,e7_17_2_1__funct_5)).
thf(s2_funct_1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ( ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( r2_hidden @ C @ B ) & ( A @ C @ D ) & ( A @ C @ E ) ) => ( = @ D @ E ) ) & ! [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(funct_1,s2_funct_1)).
thf(e9_17_2_1__funct_5,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ c3_17_2_1__funct_5 ) & ! [B: $i] : ( ( r2_hidden @ B @ c3_17_2_1__funct_5 ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ C @ ( k1_funct_1 @ c1_17__funct_5 @ ( k1_xtuple_0 @ B ) ) ) & ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ C @ ( k2_xtuple_0 @ B ) ) ) ) ) ) ),file(funct_5,e9_17_2_1__funct_5)).
