% This is the TPTP encoding of the following higher-order step in the Mizar proof of Separation from Replacement
%  at http://grid01.ciirc.cvut.cz/~mptp/mml5.29.1227/html/xboole_0.html#S1
% You can run Satallax on it using SystemOnTPTP: http://tptp.org/cgi-bin/SystemOnTPTP
%
%  consider X being set such that
%  A2: for x being object holds
%       ( x in X iff ex y being object st
%	( y in F1() & S1[y,x] ) ) from TARSKI:sch 1(A1);


thf(r2_hidden_type,type,(r2_hidden: $i>$i>$o)).
thf(c1_21_type, type, c1_21__mtest1: $i).
thf(c2_21_type, type, c2_21__mtest1: $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $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_funct_1, axiom, $true, file(funct_1, k1_funct_1)).
thf(dt_c1_21__mtest1, axiom, $true, file(mtest1, c1_21__mtest1)).
thf(dt_c2_21__mtest1, axiom,  ( (v1_relat_1 @ c2_21__mtest1)  &  (v1_funct_1 @ c2_21__mtest1) ) , file(mtest1, c2_21__mtest1)).
thf(rc1_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) , file(funct_1, rc1_funct_1)).
thf(s1_xboole_0, axiom,  (! [A: $i > $o] :  (! [B: $i] :  (? [C: $i] :  (! [D: $i] :  ( ( (r2_hidden @ D)  @ C)  <=>  ( ( (r2_hidden @ D)  @ B)  &  (A @ D) ) ) ) ) ) ) , file(xboole_0, s1_xboole_0)).
thf(e4_21__mtest1, conjecture,  (? [A: $i] :  (! [B: $i] :  ( ( (r2_hidden @ B)  @ A)  <=>  ( ( (r2_hidden @ B)  @ c1_21__mtest1)  &  (! [C: $i] :  ~ ( ( ( (= @ C)  @  ( (k1_funct_1 @ c2_21__mtest1)  @ B) )  &  ( (r2_hidden @ B)  @ C) ) ) ) ) ) ) ) , file(mtest1, e4_21__mtest1)).