% Mizar problem: t45_xtuple_0,xtuple_0,875,5 
fof(t45_xtuple_0, conjecture,  (! [A] :  (! [B] : r1_tarski(k4_xboole_0(k14_xtuple_0(A), k14_xtuple_0(B)), k14_xtuple_0(k4_xboole_0(A, B)))) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc1_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => v1_xtuple_0(A)) ) ).
fof(cc2_xtuple_0, axiom,  (! [A] :  (v3_xtuple_0(A) => v2_xtuple_0(A)) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(d14_xtuple_0, axiom,  (! [A] : k11_xtuple_0(A)=k9_xtuple_0(k9_xtuple_0(A))) ).
fof(d17_xtuple_0, axiom,  (! [A] : k14_xtuple_0(A)=k10_xtuple_0(k11_xtuple_0(A))) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] : k3_xtuple_0(A, B, C)=k4_tarski(k4_tarski(A, B), C)) ) ) ).
fof(d5_tarski, axiom,  (! [A] :  (! [B] : k4_tarski(A, B)=k2_tarski(k2_tarski(A, B), k1_tarski(A))) ) ).
fof(d5_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k4_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) &  ~ (r2_hidden(D, B)) ) ) ) ) ) ) ) ).
fof(d8_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k6_xtuple_0(A, B, C, D)=k4_tarski(k3_xtuple_0(A, B, C), D)) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_xtuple_0, axiom, $true).
fof(dt_k14_xtuple_0, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k3_xtuple_0, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k6_xtuple_0, axiom, $true).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc2_xtuple_0, axiom,  (! [A, B, C] : v2_xtuple_0(k3_xtuple_0(A, B, C))) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc3_xtuple_0, axiom,  (! [A, B, C, D] : v3_xtuple_0(k6_xtuple_0(A, B, C, D))) ).
fof(fc4_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc6_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k11_xtuple_0(A))) ) ).
fof(fc9_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k14_xtuple_0(A))) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xtuple_0, axiom,  (? [A] : v2_xtuple_0(A)) ).
fof(rc3_xtuple_0, axiom,  (? [A] : v3_xtuple_0(A)) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t20_xtuple_0, axiom,  (! [A] :  (! [B] :  ~ ( (r2_hidden(A, k14_xtuple_0(B)) &  (! [C] :  (! [D] :  (! [E] :  ~ (r2_hidden(k6_xtuple_0(C, A, D, E), B)) ) ) ) ) ) ) ) ).
fof(t21_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (r2_hidden(k6_xtuple_0(B, A, C, D), E) => r2_hidden(A, k14_xtuple_0(E))) ) ) ) ) ) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
