% Mizar problem: t15_int_2,int_2,556,43 
fof(t15_int_2, conjecture,  (! [A] :  (v1_int_1(A) =>  (! [B] :  (v1_int_1(B) =>  (! [C] :  (v1_int_1(C) =>  (r2_int_1(A, B, C) <=> r1_int_1(C, k6_xcmplx_0(A, B))) ) ) ) ) ) ) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(commutativity_k3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, B)=k3_xcmplx_0(B, A)) ) ).
fof(dt_k3_xcmplx_0, axiom, $true).
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(fc2_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k3_xcmplx_0(A, B))) ) ).
fof(fc6_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k3_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(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(spc7_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k3_xcmplx_0(A, B), C)=k3_xcmplx_0(A, k3_xcmplx_0(B, C))) ) ).
fof(reflexivity_r1_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => r1_int_1(A, A)) ) ).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(cc3_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(fc4_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k6_xcmplx_0(A, B))) ) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(d3_int_1, axiom,  (! [A] :  (v1_int_1(A) =>  (! [B] :  (v1_int_1(B) =>  (r1_int_1(A, B) <=>  (? [C] :  (v1_int_1(C) & B=k3_xcmplx_0(A, C)) ) ) ) ) ) ) ).
fof(d4_int_1, axiom,  (! [A] :  (v1_int_1(A) =>  (! [B] :  (v1_int_1(B) =>  (! [C] :  (v1_int_1(C) =>  (r2_int_1(A, B, C) <=> r1_int_1(C, k6_xcmplx_0(A, B))) ) ) ) ) ) ) ).
fof(d5_int_1, axiom,  (! [A] :  (v1_int_1(A) =>  (! [B] :  (v1_int_1(B) =>  (! [C] :  (v1_int_1(C) =>  (r2_int_1(A, B, C) <=>  (? [D] :  (v1_int_1(D) & k3_xcmplx_0(C, D)=k6_xcmplx_0(A, B)) ) ) ) ) ) ) ) ) ).
