include('Axioms/SET010^0.ax').
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(m2_finseq_2_type, type, m2_finseq_2: $i > $i > $i > $o).
thf(k1_euclid_type, type, k1_euclid: $i > $i).
thf(k7_euclid_type, type, k7_euclid: $i > $i > $i > $i).
thf(k9_euclid_type, type, k9_euclid: $i > $i > $i > $i).
thf(k7_real_1_type, type, k7_real_1: $i > $i > $i).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(m1_finseq_2_type, type, m1_finseq_2: $i > $i > $o).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(v6_membered_type, type, v6_membered: $i > $o).
thf(v3_membered_type, type, v3_membered: $i > $o).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(t7_euclid_4, axiom,   (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  (! [D: $i] :  ( ( ( (m2_finseq_2 @ D)  @ k1_numbers)  @  (k1_euclid @ C) )  =>  ( (= @  ( ( (k9_euclid @ C)  @ D)  @  ( (k7_real_1 @ A)  @ B) ) )  @  ( ( (k7_euclid @ C)  @  ( ( (k9_euclid @ C)  @ D)  @ A) )  @  ( ( (k9_euclid @ C)  @ D)  @ B) ) ) ) ) ) ) ) ) ) ) , file(euclid_4, t7_euclid_4)).
thf(t17_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) )  =>  (! [D: $i] :  ( ( ( (m2_finseq_2 @ D)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  (! [E: $i] :  ( ( ( (m2_finseq_2 @ E)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  (! [F: $i] :  ( ( ( (m2_finseq_2 @ F)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  (! [G: $i] :  ( ( ( (m2_finseq_2 @ G)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  ( (= @  ( ( (k7_euclid @ A)  @  ( ( (k7_euclid @ A)  @  ( ( (k7_euclid @ A)  @ B)  @ C) )  @ D) )  @  ( ( (k7_euclid @ A)  @  ( ( (k7_euclid @ A)  @ E)  @ F) )  @ G) ) )  @  ( ( (k7_euclid @ A)  @  ( ( (k7_euclid @ A)  @  ( ( (k7_euclid @ A)  @ B)  @ E) )  @  ( ( (k7_euclid @ A)  @ C)  @ F) ) )  @  ( ( (k7_euclid @ A)  @ D)  @ G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(euclidlp, t17_euclidlp)).
thf(redefinition_m2_finseq_2, axiom,   (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ A)  @ B)  <=>  ( (m1_subset_1 @ C)  @ B) ) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(redefinition_k5_numbers, axiom,   ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(fc6_membered, axiom,   (v6_membered @ k4_ordinal1) , file(membered, fc6_membered)).
thf(fc3_membered, axiom,   (v3_membered @ k1_numbers) , file(membered, fc3_membered)).
thf(dt_k9_euclid, axiom,   (! [A: $i, B: $i, C: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  &  (v1_xreal_0 @ C) ) )  =>  ( ( (m2_finseq_2 @  ( ( (k9_euclid @ A)  @ B)  @ C) )  @ k1_numbers)  @  (k1_euclid @ A) ) ) ) , file(euclid, k9_euclid)).
thf(dt_k1_euclid, axiom,   (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_finseq_2 @  (k1_euclid @ A) )  @ k1_numbers) ) ) , file(euclid, k1_euclid)).
thf(cc17_membered, axiom,   (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v7_ordinal1 @ B) ) ) ) ) , file(membered, cc17_membered)).
thf(cc14_membered, axiom,   (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xreal_0 @ B) ) ) ) ) , file(membered, cc14_membered)).
thf(t24_euclidlp, conjecture,   (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ k1_numbers)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ k1_numbers)  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @ k1_numbers)  =>  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @ k1_numbers)  =>  (! [G: $i] :  ( ( (m1_subset_1 @ G)  @ k5_numbers)  =>  (! [H: $i] :  ( ( ( (m2_finseq_2 @ H)  @ k1_numbers)  @  (k1_euclid @ G) )  =>  (! [I: $i] :  ( ( ( (m2_finseq_2 @ I)  @ k1_numbers)  @  (k1_euclid @ G) )  =>  (! [J: $i] :  ( ( ( (m2_finseq_2 @ J)  @ k1_numbers)  @  (k1_euclid @ G) )  =>  ( (= @  ( ( (k7_euclid @ G)  @  ( ( (k7_euclid @ G)  @  ( ( (k7_euclid @ G)  @  ( ( (k9_euclid @ G)  @ H)  @ A) )  @  ( ( (k9_euclid @ G)  @ I)  @ B) ) )  @  ( ( (k9_euclid @ G)  @ J)  @ C) ) )  @  ( ( (k7_euclid @ G)  @  ( ( (k7_euclid @ G)  @  ( ( (k9_euclid @ G)  @ H)  @ D) )  @  ( ( (k9_euclid @ G)  @ I)  @ E) ) )  @  ( ( (k9_euclid @ G)  @ J)  @ F) ) ) )  @  ( ( (k7_euclid @ G)  @  ( ( (k7_euclid @ G)  @  ( ( (k9_euclid @ G)  @ H)  @  ( (k7_real_1 @ A)  @ D) ) )  @  ( ( (k9_euclid @ G)  @ I)  @  ( (k7_real_1 @ B)  @ E) ) ) )  @  ( ( (k9_euclid @ G)  @ J)  @  ( (k7_real_1 @ C)  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(euclidlp, t24_euclidlp)).