% Mizar problem: e2_3_1_1,pralg_2,83,69 
include('Axioms/SET010^0.ax').
thf(c1_3_type,type,( c1_3__pralg_2: $i )).
thf(k10_funct_6_type,type,( k10_funct_6: $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(v1_funcop_1_type,type,( v1_funcop_1: $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(v2_funcop_1_type,type,( v2_funcop_1: $i > $o )).
thf(cc2_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funcop_1 @ A ) ) ) ),file(funcop_1,cc2_funcop_1)).
thf(rc1_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ),file(funcop_1,rc1_funcop_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k10_funct_6,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k10_funct_6 @ A ) ) & ( v1_funct_1 @ ( k10_funct_6 @ A ) ) & ( v1_funcop_1 @ ( k10_funct_6 @ A ) ) ) ) ),file(funct_6,k10_funct_6)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_3__pralg_2,axiom,( ( v1_relat_1 @ c1_3__pralg_2 ) & ( v1_funct_1 @ c1_3__pralg_2 ) ),file(pralg_2,c1_3__pralg_2)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e1_3_1_1__pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ A @ D ) & ( = @ B @ ( k10_funct_6 @ D ) ) ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ A @ D ) & ( = @ C @ ( k10_funct_6 @ D ) ) ) ) => ( = @ B @ C ) ) ),file(pralg_2,e1_3_1_1__pralg_2)).
thf(s1_tarski,axiom,( ! [A: $i] : ! [B: $i > $i > $o] : ( ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( B @ C @ D ) & ( B @ C @ E ) ) => ( = @ D @ E ) ) => ? [C: $i] : ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ? [E: $i] : ( ( r2_hidden @ E @ A ) & ( B @ E @ D ) ) ) ) ),file(tarski,s1_tarski)).
thf(e2_3_1_1__pralg_2,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ? [C: $i] : ( ( r2_hidden @ C @ ( k9_xtuple_0 @ c1_3__pralg_2 ) ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ C @ D ) & ( = @ B @ ( k10_funct_6 @ D ) ) ) ) ) ),file(pralg_2,e2_3_1_1__pralg_2)).
