% Mizar problem: t43_xxreal_3,xxreal_3,1680,5 
fof(t43_xxreal_3, conjecture,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (v1_xxreal_0(C) =>  (r2_hidden(C, k1_numbers) =>  (r1_xxreal_0(B, A) |  ( ~ (r1_xxreal_0(k1_xxreal_3(B, C), k1_xxreal_3(A, C)))  &  ~ (r1_xxreal_0(k3_xxreal_3(B, C), k3_xxreal_3(A, C))) ) ) ) ) ) ) ) ) ) ).
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_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc2_xcmplx_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xcmplx_0(A)) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(commutativity_k1_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k1_xxreal_3(A, B)=k1_xxreal_3(B, A)) ) ).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d4_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) => k3_xxreal_3(A, B)=k1_xxreal_3(A, k2_xxreal_3(B))) ) ) ) ).
fof(d7_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) =>  (! [B] :  (v1_xcmplx_0(B) => k6_xcmplx_0(A, B)=k2_xcmplx_0(A, k4_xcmplx_0(B))) ) ) ) ).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k1_xxreal_3(A, B))) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => v1_xxreal_0(k2_xxreal_3(A))) ) ).
fof(dt_k3_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k3_xxreal_3(A, B))) ) ).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_xxreal_3, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xxreal_0(k2_xxreal_3(A)) & v1_xreal_0(k2_xxreal_3(A))) ) ) ).
fof(fc2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(fc2_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) & v1_xreal_0(k1_xxreal_3(A, B))) ) ) ).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc3_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (v1_xxreal_0(k3_xxreal_3(A, B)) & v1_xreal_0(k3_xxreal_3(A, B))) ) ) ).
fof(fc4_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k6_xcmplx_0(A, B))) ) ).
fof(fc4_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) &  (v1_xxreal_0(B) &  ~ (v1_xreal_0(B)) ) )  =>  ~ (v1_xreal_0(k1_xxreal_3(A, B))) ) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc7_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k6_xcmplx_0(A, B))) ) ).
fof(ie1_xxreal_3, axiom,  (! [A, B, C, D] :  ( (v1_xreal_0(A) &  (v1_xreal_0(B) &  (v1_xcmplx_0(C) & v1_xcmplx_0(D)) ) )  =>  ( (A=C & B=D)  => k1_xxreal_3(A, B)=k2_xcmplx_0(C, D)) ) ) ).
fof(ie2_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xcmplx_0(B))  =>  (A=B => k2_xxreal_3(A)=k4_xcmplx_0(B)) ) ) ).
fof(ie3_xxreal_3, axiom,  (! [A, B, C, D] :  ( (v1_xreal_0(A) &  (v1_xreal_0(B) &  (v1_xcmplx_0(C) & v1_xcmplx_0(D)) ) )  =>  ( (A=C & B=D)  => k3_xxreal_3(A, B)=k6_xcmplx_0(C, D)) ) ) ).
fof(involutiveness_k2_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => k2_xxreal_3(k2_xxreal_3(A))=A) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(rc1_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(spc1_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, k4_xcmplx_0(B))=k6_xcmplx_0(A, B)) ) ).
fof(spc6_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k2_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(A, k2_xcmplx_0(B, C))) ) ).
fof(spc8_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k4_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(spc9_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k6_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k6_xcmplx_0(B, A)) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_xxreal_0, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  ( (r1_xxreal_0(A, B) & r1_xxreal_0(B, A))  => A=B) ) ) ) ) ).
fof(t22_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (v1_xreal_0(A) =>  (k1_xxreal_3(k3_xxreal_3(B, A), A)=B & k3_xxreal_3(k1_xxreal_3(B, A), A)=B) ) ) ) ) ) ).
fof(t36_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (v1_xxreal_0(C) =>  (! [D] :  (v1_xxreal_0(D) =>  ( (r1_xxreal_0(A, B) & r1_xxreal_0(C, D))  => r1_xxreal_0(k1_xxreal_3(A, C), k1_xxreal_3(B, D))) ) ) ) ) ) ) ) ) ).
