include('Axioms/SET010^0.ax').
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k1_sgraph1_type, type, k1_sgraph1: $i > $i > $i).
thf(n1_type, type, 1: $i).
thf(k2_finseq_1_type, type, k2_finseq_1: $i > $i).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(r1_xxreal_0_type, type, r1_xxreal_0: $i > $i > $o).
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_numbers_type, type, k1_numbers: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(r1_tarski_type, type, r1_tarski: $i > $i > $o).
thf(t4_subset, axiom,   (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r2_hidden @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t1_finseq_1, axiom,   (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( ( (r2_hidden @ A)  @  (k2_finseq_1 @ B) )  <=>  ( ( (r1_xxreal_0 @ 1)  @ A)  &  ( (r1_xxreal_0 @ A)  @ B) ) ) ) ) ) ) , file(finseq_1, t1_finseq_1)).
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_k5_numbers, axiom,   ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(dt_k2_finseq_1, axiom,   (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_subset_1 @  (k2_finseq_1 @ A) )  @  (k1_zfmisc_1 @ k5_numbers) ) ) ) , file(finseq_1, k2_finseq_1)).
thf(d3_tarski, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (r1_tarski @ A)  @ B)  <=>  (! [C: $i] :  ( ( (r2_hidden @ C)  @ A)  =>  ( (r2_hidden @ C)  @ B) ) ) ) ) ) , file(tarski, d3_tarski)).
thf(d1_sgraph1, axiom,   (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( (= @  ( (k1_sgraph1 @ A)  @ B) )  @  ( ( (replSep1 @  (^ [C: $i] :  ( (m1_subset_1 @ C)  @ k5_numbers) ) )  @  (^ [C: $i] : C) )  @  (^ [C: $i] :  ( ( (r1_xxreal_0 @ A)  @ C)  &  ( (r1_xxreal_0 @ C)  @ B) ) ) ) ) ) ) ) ) , file(sgraph1, d1_sgraph1)).
thf(d10_xboole_0, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (= @ A)  @ B)  <=>  ( ( (r1_tarski @ A)  @ B)  &  ( (r1_tarski @ B)  @ A) ) ) ) ) , file(xboole_0, d10_xboole_0)).
thf(cc8_ordinal1, axiom,   (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(t3_sgraph1, conjecture,   (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ( (= @  ( (k1_sgraph1 @ 1)  @ A) )  @  (k2_finseq_1 @ A) ) ) ) , file(sgraph1, t3_sgraph1)).