% Mizar problem: e3_7_1,funct_3,165,31 
include('Axioms/SET010^0.ax').
thf(f1_s2_funct_3_type,type,( f1_s2_funct_3: $i )).
thf(f2_s2_funct_3_type,type,( f2_s2_funct_3: $i )).
thf(f3_s2_funct_3_type,type,( f3_s2_funct_3: $i > $i > $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_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_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_f1_s2_funct_3,axiom,( $true ),file(funct_3,f1_s2_funct_3)).
thf(dt_f2_s2_funct_3,axiom,( $true ),file(funct_3,f2_s2_funct_3)).
thf(dt_f3_s2_funct_3,axiom,( $true ),file(funct_3,f3_s2_funct_3)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e2_7_1__funct_3,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( r2_hidden @ A @ f1_s2_funct_3 ) & ( r2_hidden @ B @ f2_s2_funct_3 ) & ( = @ C @ ( f3_s2_funct_3 @ A @ B ) ) & ( = @ D @ ( f3_s2_funct_3 @ A @ B ) ) ) => ( = @ C @ D ) ) ),file(funct_3,e2_7_1__funct_3)).
thf(e1_7_1__funct_3,axiom,( ! [A: $i] : ! [B: $i] : ~ ( ( r2_hidden @ A @ f1_s2_funct_3 ) & ( r2_hidden @ B @ f2_s2_funct_3 ) & ! [C: $i] : ~ ( = @ C @ ( f3_s2_funct_3 @ A @ B ) ) ) ),file(funct_3,e1_7_1__funct_3)).
thf(s1_funct_3,axiom,( ! [A: $i > $i > $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ! [D: $i] : ! [E: $i] : ! [F: $i] : ! [G: $i] : ( ( ( r2_hidden @ D @ C ) & ( r2_hidden @ E @ B ) & ( A @ D @ E @ F ) & ( A @ D @ E @ G ) ) => ( = @ F @ G ) ) & ! [D: $i] : ! [E: $i] : ~ ( ( r2_hidden @ D @ C ) & ( r2_hidden @ E @ B ) & ! [F: $i] : ~ ( A @ D @ E @ F ) ) ) => ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ ( k9_xtuple_0 @ D ) @ ( k2_zfmisc_1 @ C @ B ) ) & ! [E: $i] : ! [F: $i] : ( ( ( r2_hidden @ E @ C ) & ( r2_hidden @ F @ B ) ) => ( A @ E @ F @ ( k1_binop_1 @ D @ E @ F ) ) ) ) ) ),file(funct_3,s1_funct_3)).
thf(e3_7_1__funct_3,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k2_zfmisc_1 @ f1_s2_funct_3 @ f2_s2_funct_3 ) ) & ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ B @ f1_s2_funct_3 ) & ( r2_hidden @ C @ f2_s2_funct_3 ) ) => ( = @ ( k1_binop_1 @ A @ B @ C ) @ ( f3_s2_funct_3 @ B @ C ) ) ) ) ),file(funct_3,e3_7_1__funct_3)).
