% Mizar problem: e4_161_1_1_2,funct_1,3369,56 
include('Axioms/SET010^0.ax').
thf(f1_s5_funct_1_type,type,( f1_s5_funct_1: $i )).
thf(f2_s5_funct_1_type,type,( f2_s5_funct_1: $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(p1_s5_funct_1_type,type,( p1_s5_funct_1: $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_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_f1_s5_funct_1,axiom,( $true ),file(funct_1,f1_s5_funct_1)).
thf(dt_f2_s5_funct_1,axiom,( $true ),file(funct_1,f2_s5_funct_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e2_161_1_1_2__funct_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ f1_s5_funct_1 ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) <=> ( ( r2_hidden @ D @ f2_s5_funct_1 ) & ( p1_s5_funct_1 @ A @ D ) ) ) & ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( r2_hidden @ D @ f2_s5_funct_1 ) & ( p1_s5_funct_1 @ A @ D ) ) ) ) => ( = @ B @ C ) ) ),file(funct_1,e2_161_1_1_2__funct_1)).
thf(e3_161_1_1_2__funct_1,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ f1_s5_funct_1 ) & ! [B: $i] : ~ ( ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ( ( r2_hidden @ C @ f2_s5_funct_1 ) & ( p1_s5_funct_1 @ A @ C ) ) ) ) ) ),file(funct_1,e3_161_1_1_2__funct_1)).
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(e4_161_1_1_2__funct_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ f1_s5_funct_1 ) & ! [B: $i] : ( ( r2_hidden @ B @ f1_s5_funct_1 ) => ! [C: $i] : ( ( r2_hidden @ C @ ( k1_funct_1 @ A @ B ) ) <=> ( ( r2_hidden @ C @ f2_s5_funct_1 ) & ( p1_s5_funct_1 @ B @ C ) ) ) ) ) ),file(funct_1,e4_161_1_1_2__funct_1)).
