include('Axioms/SET010^0.ax').
thf(m2_finseq_2_type, type, m2_finseq_2: $i > $i > $i > $o).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_euclid_type, type, k1_euclid: $i > $i).
thf(n3_type, type, 3: $i).
thf(k23_rvsum_1_type, type, k23_rvsum_1: $i > $i > $i).
thf(k1_euclid_8_type, type, k1_euclid_8: $i > $i > $i > $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k2_finseq_2_type, type, k2_finseq_2: $i > $i > $i).
thf(k11_finseq_1_type, type, k11_finseq_1: $i > $i > $i > $i).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(k5_euclid_type, type, k5_euclid: $i > $i).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(m2_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(n0_type, type, 0: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k5_finseq_2_type, type, k5_finseq_2: $i > $i > $i > $i).
thf(k4_euclid_type, type, k4_euclid: $i > $i).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(v1_xcmplx_0_type, type, v1_xcmplx_0: $i > $o).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(c7_type, type, c7__xreal_0: $i).
thf(c2_type, type, c2__topalg_3: $i).
thf(c1_type, type, c1__xreal_1: $i).
thf(c1_type, type, c1__xreal_0: $i).
thf(t6_boole, axiom,   (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (= @ A)  @ k1_xboole_0) ) ) , file(boole, t6_boole)).
thf(t62_finseq_2, axiom,   (! [A: $i] :  ( (= @  ( (k2_finseq_2 @ 3)  @ A) )  @  ( ( (k11_finseq_1 @ A)  @ A)  @ A) ) ) , file(finseq_2, t62_finseq_2)).
thf(t18_euclid_4, axiom,   (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( ( (m2_finseq_2 @ B)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  ( (= @  ( (k23_rvsum_1 @ B)  @  (k5_euclid @ A) ) )  @ k6_numbers) ) ) ) ) , file(euclid_4, t18_euclid_4)).
thf(spc3_numerals, axiom,   ( ( (v2_xxreal_0 @ 3)  &  ( ( (m2_subset_1 @ 3)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ 3)  @ k5_numbers)  &  ( (m1_subset_1 @ 3)  @ k1_numbers) ) ) , file(numerals, spc3_numerals)).
thf(spc0_numerals, axiom,   ( ( ( (m2_subset_1 @ 0)  @ k1_numbers)  @ k5_numbers)  &  ( ( (m1_subset_1 @ 0)  @ k5_numbers)  &  ( (m1_subset_1 @ 0)  @ k1_numbers) ) ) , file(numerals, spc0_numerals)).
thf(spc0_boole, axiom,   (v1_xboole_0 @ 0) , file(boole, spc0_boole)).
thf(redefinition_k6_numbers, axiom,   ( (= @ k6_numbers)  @ k1_xboole_0) , file(numbers, k6_numbers)).
thf(redefinition_k5_numbers, axiom,   ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k5_finseq_2, axiom,   (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v7_ordinal1 @ B)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( (= @  ( ( (k5_finseq_2 @ A)  @ B)  @ C) )  @  ( (k2_finseq_2 @ B)  @ C) ) ) ) , file(finseq_2, k5_finseq_2)).
thf(redefinition_k5_euclid, axiom,   (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k5_euclid @ A) )  @  (k4_euclid @ A) ) ) ) , file(euclid, k5_euclid)).
thf(redefinition_k1_euclid_8, axiom,   (! [A: $i, B: $i, C: $i] :  ( ( (v1_xreal_0 @ A)  &  ( (v1_xreal_0 @ B)  &  (v1_xreal_0 @ C) ) )  =>  ( (= @  ( ( (k1_euclid_8 @ A)  @ B)  @ C) )  @  ( ( (k11_finseq_1 @ A)  @ B)  @ C) ) ) ) , file(euclid_8, k1_euclid_8)).
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(fc1_numbers, axiom,   ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers)).
thf(de_c7__xreal_0, axiom,   ( (= @ c7__xreal_0)  @ k6_numbers) , file(xreal_0, c7__xreal_0)).
thf(de_c2__topalg_3, axiom,   ( (= @ c2__topalg_3)  @ k6_numbers) , file(topalg_3, c2__topalg_3)).
thf(de_c1__xreal_1, axiom,   ( (= @ c1__xreal_1)  @ k6_numbers) , file(xreal_1, c1__xreal_1)).
thf(de_c1__xreal_0, axiom,   ( (= @ c1__xreal_0)  @ k6_numbers) , file(xreal_0, c1__xreal_0)).
thf(d4_euclid, axiom,   (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k4_euclid @ A) )  @  ( ( (k5_finseq_2 @ k1_numbers)  @ A)  @ k6_numbers) ) ) ) , file(euclid, d4_euclid)).
thf(cc8_ordinal1, axiom,   (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(t13_euclid_8, conjecture,   (! [A: $i] :  ( ( ( (m2_finseq_2 @ A)  @ k1_numbers)  @  (k1_euclid @ 3) )  =>  ( (= @  ( (k23_rvsum_1 @ A)  @  ( ( (k1_euclid_8 @ k6_numbers)  @ k6_numbers)  @ k6_numbers) ) )  @ k6_numbers) ) ) , file(euclid_8, t13_euclid_8)).