include('Axioms/SET010^0.ax').
thf(v1_int_1_type, type, v1_int_1: $i > $o).
thf(r1_xxreal_0_type, type, r1_xxreal_0: $i > $i > $o).
thf(n1_type, type, 1: $i).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o).
thf(m2_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(v1_xcmplx_0_type, type, v1_xcmplx_0: $i > $o).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(t6_real, axiom,   (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v1_xboole_0 @ A)  |  ( (v2_xxreal_0 @ B)  |  (v3_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t6_real)).
thf(t6_boole, axiom,   (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (= @ A)  @ k1_xboole_0) ) ) , file(boole, t6_boole)).
thf(spc1_numerals, axiom,   ( ( (v2_xxreal_0 @ 1)  &  ( ( (m2_subset_1 @ 1)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ 1)  @ k5_numbers)  &  ( (m1_subset_1 @ 1)  @ k1_numbers) ) ) , file(numerals, spc1_numerals)).
thf(redefinition_k6_numbers, axiom,   ( (= @ k6_numbers)  @ k1_xboole_0) , file(numbers, k6_numbers)).
thf(rc4_xreal_0, axiom,   (? [A: $i] :  ( (v1_xboole_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)).
thf(l13_int_1, axiom,   (! [A: $i] :  ( (v1_int_1 @ A)  =>  ( ~ ( ( (r1_xxreal_0 @ A)  @ k6_numbers) )  =>  ( (r1_xxreal_0 @ 1)  @ A) ) ) ) , file(int_1, l13_int_1)).
thf(cc4_xreal_0, axiom,   (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)).
thf(cc3_xxreal_0, axiom,   (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc3_xxreal_0)).
thf(cc3_int_1, axiom,   (! [A: $i] :  ( (v1_int_1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(int_1, cc3_int_1)).
thf(cc2_nat_1, axiom,   (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ~ ( (v3_xxreal_0 @ A) ) ) ) , file(nat_1, cc2_nat_1)).
thf(cc1_xreal_0, axiom,   (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0)).
thf(l1_euler_2, conjecture,   (! [A: $i] :  ( (v1_int_1 @ A)  =>  ( ~ ( ( (r1_xxreal_0 @ 1)  @ A) )  <=>  ( (r1_xxreal_0 @ A)  @ k1_xboole_0) ) ) ) , file(euler_2, l1_euler_2)).