include('Axioms/SET010^0.ax').
thf(r1_lang1_type, type, r1_lang1: $i > $i > $i > $o).
thf(k5_dtconstr_type, type, k5_dtconstr: $i).
thf(c3_type, type, c3__dtconstr: $i).
thf(k3_pre_poly_type, type, k3_pre_poly: $i > $i > $i).
thf(u1_struct_0_type, type, u1_struct_0: $i > $i).
thf(c2_type, type, c2__dtconstr: $i).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(n1_type, type, 1: $i).
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(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(k7_domain_1_type, type, k7_domain_1: $i > $i > $i > $i).
thf(k2_tarski_type, type, k2_tarski: $i > $i > $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k5_finseq_1_type, type, k5_finseq_1: $i > $i).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(m1_finseq_2_type, type, m1_finseq_2: $i > $i > $o).
thf(m2_finseq_2_type, type, m2_finseq_2: $i > $i > $i > $o).
thf(m2_finseq_1_type, type, m2_finseq_1: $i > $i > $o).
thf(v2_struct_0_type, type, v2_struct_0: $i > $o).
thf(v1_lang1_type, type, v1_lang1: $i > $o).
thf(l1_lang1_type, type, l1_lang1: $i > $o).
thf(k3_finseq_2_type, type, k3_finseq_2: $i > $i).
thf(k4_tarski_type, type, k4_tarski: $i > $i > $i).
thf(k1_tarski_type, type, k1_tarski: $i > $i).
thf(t1_numerals, axiom,   ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
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_k7_domain_1, axiom,   (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( (= @  ( ( (k7_domain_1 @ A)  @ B)  @ C) )  @  ( (k2_tarski @ B)  @ C) ) ) ) , file(domain_1, k7_domain_1)).
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_k3_pre_poly, axiom,   (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( (= @  ( (k3_pre_poly @ A)  @ B) )  @  (k5_finseq_1 @ B) ) ) ) , file(pre_poly, k3_pre_poly)).
thf(fc6_ordinal1, axiom,   ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc3_xboole_0, axiom,   (! [A: $i, B: $i] :  ~ ( (v1_xboole_0 @  ( (k2_tarski @ A)  @ B) ) ) ) , file(xboole_0, fc3_xboole_0)).
thf(dt_m2_finseq_2, axiom,   (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ A)  @ B)  =>  ( (m2_finseq_1 @ C)  @ A) ) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(dt_k5_dtconstr, axiom,   ( ~ ( (v2_struct_0 @ k5_dtconstr) )  &  ( (v1_lang1 @ k5_dtconstr)  &  (l1_lang1 @ k5_dtconstr) ) ) , file(dtconstr, k5_dtconstr)).
thf(dt_k3_pre_poly, axiom,   (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( ( (m2_finseq_2 @  ( (k3_pre_poly @ A)  @ B) )  @ A)  @  (k3_finseq_2 @ A) ) ) ) , file(pre_poly, k3_pre_poly)).
thf(dt_k3_finseq_2, axiom,   (! [A: $i] :  ( (m1_finseq_2 @  (k3_finseq_2 @ A) )  @ A) ) , file(finseq_2, k3_finseq_2)).
thf(dt_c3__dtconstr, axiom,   ( (m1_subset_1 @ c3__dtconstr)  @  (u1_struct_0 @ k5_dtconstr) ) , file(dtconstr, c3__dtconstr)).
thf(dt_c2__dtconstr, axiom,   ( (m1_subset_1 @ c2__dtconstr)  @  (u1_struct_0 @ k5_dtconstr) ) , file(dtconstr, c2__dtconstr)).
thf(de_c3__dtconstr, axiom,   ( (= @ c3__dtconstr)  @ 1) , file(dtconstr, c3__dtconstr)).
thf(de_c2__dtconstr, axiom,   ( (= @ c2__dtconstr)  @ k6_numbers) , file(dtconstr, c2__dtconstr)).
thf(d5_tarski, axiom,   (! [A: $i] :  (! [B: $i] :  ( (= @  ( (k4_tarski @ A)  @ B) )  @  ( (k2_tarski @  ( (k2_tarski @ A)  @ B) )  @  (k1_tarski @ A) ) ) ) ) , file(tarski, d5_tarski)).
thf(d5_finseq_1, axiom,   (! [A: $i] :  ( (= @  (k5_finseq_1 @ A) )  @  (k1_tarski @  ( (k4_tarski @ 1)  @ A) ) ) ) , file(finseq_1, d5_finseq_1)).
thf(d2_dtconstr, axiom,   (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v1_lang1 @ A)  &  (l1_lang1 @ A) ) )  =>  ( ( (= @ A)  @ k5_dtconstr)  <=>  ( ( (= @  (u1_struct_0 @ A) )  @  ( ( (k7_domain_1 @ k5_numbers)  @ k6_numbers)  @ 1) )  &  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m2_finseq_1 @ C)  @  (u1_struct_0 @ A) )  =>  ( ( ( (r1_lang1 @ A)  @ B)  @ C)  <=>  ( ( (= @ B)  @ 1)  &  ( ( (= @ C)  @  ( (k3_pre_poly @ k5_numbers)  @ k6_numbers) )  |  ( (= @ C)  @  ( (k3_pre_poly @ k5_numbers)  @ 1) ) ) ) ) ) ) ) ) ) ) ) ) , file(dtconstr, d2_dtconstr)).
thf(l14_dtconstr, conjecture,   ( ( (r1_lang1 @ k5_dtconstr)  @ c3__dtconstr)  @  ( (k3_pre_poly @  (u1_struct_0 @ k5_dtconstr) )  @ c2__dtconstr) ) , file(dtconstr, l14_dtconstr)).