% Mizar problem: e3_2_1_1,funcop_1,109,72 
include('Axioms/SET010^0.ax').
thf(c1_2_type,type,( c1_2__funcop_1: $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(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
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_2__funcop_1,axiom,( ( v1_relat_1 @ c1_2__funcop_1 ) & ( v1_funct_1 @ c1_2__funcop_1 ) ),file(funcop_1,c1_2__funcop_1)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e2_2_1_1__funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c1_2__funcop_1 ) ) & ! [D: $i] : ! [E: $i] : ( ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ A ) @ ( k4_tarski @ D @ E ) ) => ( = @ B @ ( k4_tarski @ E @ D ) ) ) & ~ ( ~ ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ A ) @ B ) & ! [D: $i] : ! [E: $i] : ~ ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ A ) @ ( k4_tarski @ D @ E ) ) ) & ! [D: $i] : ! [E: $i] : ( ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ A ) @ ( k4_tarski @ D @ E ) ) => ( = @ C @ ( k4_tarski @ E @ D ) ) ) & ~ ( ~ ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ A ) @ C ) & ! [D: $i] : ! [E: $i] : ~ ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ A ) @ ( k4_tarski @ D @ E ) ) ) ) => ( = @ B @ C ) ) ),file(funcop_1,e2_2_1_1__funcop_1)).
thf(e1_2_1_1__funcop_1,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c1_2__funcop_1 ) ) & ! [B: $i] : ~ ( ! [C: $i] : ! [D: $i] : ( ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ A ) @ ( k4_tarski @ C @ D ) ) => ( = @ B @ ( k4_tarski @ D @ C ) ) ) & ~ ( ~ ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ A ) @ B ) & ! [C: $i] : ! [D: $i] : ~ ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ A ) @ ( k4_tarski @ C @ D ) ) ) ) ) ),file(funcop_1,e1_2_1_1__funcop_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(e3_2_1_1__funcop_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k9_xtuple_0 @ c1_2__funcop_1 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c1_2__funcop_1 ) ) => ( ! [C: $i] : ! [D: $i] : ( ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ B ) @ ( k4_tarski @ C @ D ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k4_tarski @ D @ C ) ) ) & ~ ( ~ ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ B ) @ ( k1_funct_1 @ A @ B ) ) & ! [C: $i] : ! [D: $i] : ~ ( = @ ( k1_funct_1 @ c1_2__funcop_1 @ B ) @ ( k4_tarski @ C @ D ) ) ) ) ) ) ),file(funcop_1,e3_2_1_1__funcop_1)).
