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(k7_euclid_8_type, type, k7_euclid_8: $i > $i > $i > $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k23_rvsum_1_type, type, k23_rvsum_1: $i > $i > $i).
thf(k16_euclid_type, type, k16_euclid: $i > $i).
thf(r3_euclidlp_type, type, r3_euclidlp: $i > $i > $i > $o).
thf(k5_euclid_8_type, type, k5_euclid_8: $i > $i > $i).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(k5_numbers_type, type, k5_numbers: $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(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(t71_euclid_8, axiom,   (! [A: $i] :  ( ( ( (m2_finseq_2 @ A)  @ k1_numbers)  @  (k1_euclid @ 3) )  =>  ( (= @  ( (k23_rvsum_1 @ A)  @  (k16_euclid @ 3) ) )  @ k6_numbers) ) ) , file(euclid_8, t71_euclid_8)).
thf(t3_euclid_8, axiom,   (! [A: $i] :  ( ( ( (m2_finseq_2 @ A)  @ k1_numbers)  @  (k1_euclid @ 3) )  =>  (! [B: $i] :  ( ( ( (m2_finseq_2 @ B)  @ k1_numbers)  @  (k1_euclid @ 3) )  =>  ( ~ ( ( ( (r3_euclidlp @ 3)  @ A)  @ B) )  =>  ( (= @  ( (k5_euclid_8 @ A)  @ B) )  @  (k16_euclid @ 3) ) ) ) ) ) ) , file(euclid_8, t3_euclid_8)).
thf(t37_euclidlp, axiom,   (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  (! [B: $i] :  ( ( ( (m2_finseq_2 @ B)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  ~ ( ( ( ( (r3_euclidlp @ A)  @ B)  @ C)  &  ( (= @ B)  @ C) ) ) ) ) ) ) ) ) , file(euclidlp, t37_euclidlp)).
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(redefinition_k6_numbers, axiom,   ( (= @ k6_numbers)  @ k1_xboole_0) , file(numbers, k6_numbers)).
thf(d6_euclid_8, axiom,   (! [A: $i] :  ( ( ( (m2_finseq_2 @ A)  @ k1_numbers)  @  (k1_euclid @ 3) )  =>  (! [B: $i] :  ( ( ( (m2_finseq_2 @ B)  @ k1_numbers)  @  (k1_euclid @ 3) )  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ k1_numbers)  @  (k1_euclid @ 3) )  =>  ( (= @  ( ( (k7_euclid_8 @ A)  @ B)  @ C) )  @  ( (k23_rvsum_1 @ A)  @  ( (k5_euclid_8 @ B)  @ C) ) ) ) ) ) ) ) ) , file(euclid_8, d6_euclid_8)).
thf(t92_euclid_8, conjecture,   (! [A: $i] :  ( ( ( (m2_finseq_2 @ A)  @ k1_numbers)  @  (k1_euclid @ 3) )  =>  (! [B: $i] :  ( ( ( (m2_finseq_2 @ B)  @ k1_numbers)  @  (k1_euclid @ 3) )  =>  ( (= @  ( ( (k7_euclid_8 @ A)  @ B)  @ B) )  @ k6_numbers) ) ) ) ) , file(euclid_8, t92_euclid_8)).