% Mizar problem: e3_1,partfun1,72,66 
include('Axioms/SET010^0.ax').
thf(c1_1_type,type,( c1_1__partfun1: $i )).
thf(c2_1_type,type,( c2_1__partfun1: $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $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(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(commutativity_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ A ) ) ),file(xboole_0,k2_xboole_0)).
thf(idempotence_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k2_xboole_0)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
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_1__partfun1,axiom,( ( v1_relat_1 @ c1_1__partfun1 ) & ( v1_funct_1 @ c1_1__partfun1 ) ),file(partfun1,c1_1__partfun1)).
thf(dt_c2_1__partfun1,axiom,( ( v1_relat_1 @ c2_1__partfun1 ) & ( v1_funct_1 @ c2_1__partfun1 ) ),file(partfun1,c2_1__partfun1)).
thf(fc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) ) => ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(relat_1,fc3_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_1__partfun1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_xboole_0 @ c1_1__partfun1 @ c2_1__partfun1 ) ) & ( r2_hidden @ ( k4_tarski @ A @ C ) @ ( k2_xboole_0 @ c1_1__partfun1 @ c2_1__partfun1 ) ) ) => ( = @ B @ C ) ) ),file(partfun1,e2_1__partfun1)).
thf(s1_funct_1,axiom,( ! [A: $i] : ! [B: $i > $i > $o] : ( ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( B @ C @ D ) & ( B @ C @ E ) ) => ( = @ D @ E ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ! [D: $i] : ! [E: $i] : ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) <=> ( ( r2_hidden @ D @ A ) & ( B @ D @ E ) ) ) ) ) ),file(funct_1,s1_funct_1)).
thf(e3_1__partfun1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ! [B: $i] : ! [C: $i] : ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) <=> ( ( r2_hidden @ B @ ( k2_xboole_0 @ ( k9_xtuple_0 @ c1_1__partfun1 ) @ ( k9_xtuple_0 @ c2_1__partfun1 ) ) ) & ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k2_xboole_0 @ c1_1__partfun1 @ c2_1__partfun1 ) ) ) ) ) ),file(partfun1,e3_1__partfun1)).
