% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/FFT/prob_33__3222544_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:08:51.936

% Could-be-implicit typings (3)
thf(ty_n_t__Set__Oset_It__Nat__Onat_J, type,
    set_nat : $tType).
thf(ty_n_t__Num__Onum, type,
    num : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (16)
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Num_Onum_OBit0, type,
    bit0 : num > num).
thf(sy_c_Num_Onum_OBit1, type,
    bit1 : num > num).
thf(sy_c_Num_Onum_OOne, type,
    one : num).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat, type,
    numeral_numeral_nat : num > nat).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J, type,
    bot_bot_nat_o : nat > $o).
thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat, type,
    bot_bot_nat : nat).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J, type,
    bot_bot_set_nat : set_nat).
thf(sy_c_Set_OCollect_001t__Nat__Onat, type,
    collect_nat : (nat > $o) > set_nat).
thf(sy_c_Set_Oinsert_001t__Nat__Onat, type,
    insert_nat : nat > set_nat > set_nat).
thf(sy_c_Set_Ois__singleton_001t__Nat__Onat, type,
    is_singleton_nat : set_nat > $o).
thf(sy_c_Set_Othe__elem_001t__Nat__Onat, type,
    the_elem_nat : set_nat > nat).
thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat, type,
    set_or562006527an_nat : nat > nat > set_nat).
thf(sy_c_member_001t__Nat__Onat, type,
    member_nat : nat > set_nat > $o).

% Relevant facts (88)
thf(fact_0_calculation, axiom,
    (((set_or562006527an_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (set_or562006527an_nat @ zero_zero_nat @ (suc @ (suc @ (suc @ (suc @ zero_zero_nat)))))))). % calculation
thf(fact_1_Suc__1, axiom,
    (((suc @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % Suc_1
thf(fact_2_atLeastLessThan__singleton, axiom,
    ((![M : nat]: ((set_or562006527an_nat @ M @ (suc @ M)) = (insert_nat @ M @ bot_bot_set_nat))))). % atLeastLessThan_singleton
thf(fact_3_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_4_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_5_semiring__norm_I86_J, axiom,
    ((![M : num]: (~ (((bit1 @ M) = one)))))). % semiring_norm(86)
thf(fact_6_semiring__norm_I84_J, axiom,
    ((![N : num]: (~ ((one = (bit1 @ N))))))). % semiring_norm(84)
thf(fact_7_semiring__norm_I89_J, axiom,
    ((![M : num, N : num]: (~ (((bit1 @ M) = (bit0 @ N))))))). % semiring_norm(89)
thf(fact_8_semiring__norm_I88_J, axiom,
    ((![M : num, N : num]: (~ (((bit0 @ M) = (bit1 @ N))))))). % semiring_norm(88)
thf(fact_9_numeral__3__eq__3, axiom,
    (((numeral_numeral_nat @ (bit1 @ one)) = (suc @ (suc @ (suc @ zero_zero_nat)))))). % numeral_3_eq_3
thf(fact_10_singletonI, axiom,
    ((![A : nat]: (member_nat @ A @ (insert_nat @ A @ bot_bot_set_nat))))). % singletonI
thf(fact_11_numeral__2__eq__2, axiom,
    (((numeral_numeral_nat @ (bit0 @ one)) = (suc @ (suc @ zero_zero_nat))))). % numeral_2_eq_2
thf(fact_12_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_13_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_14_semiring__norm_I87_J, axiom,
    ((![M : num, N : num]: (((bit0 @ M) = (bit0 @ N)) = (M = N))))). % semiring_norm(87)
thf(fact_15_empty__Collect__eq, axiom,
    ((![P : nat > $o]: ((bot_bot_set_nat = (collect_nat @ P)) = (![X : nat]: (~ ((P @ X)))))))). % empty_Collect_eq
thf(fact_16_Collect__empty__eq, axiom,
    ((![P : nat > $o]: (((collect_nat @ P) = bot_bot_set_nat) = (![X : nat]: (~ ((P @ X)))))))). % Collect_empty_eq
thf(fact_17_all__not__in__conv, axiom,
    ((![A2 : set_nat]: ((![X : nat]: (~ ((member_nat @ X @ A2)))) = (A2 = bot_bot_set_nat))))). % all_not_in_conv
thf(fact_18_empty__iff, axiom,
    ((![C : nat]: (~ ((member_nat @ C @ bot_bot_set_nat)))))). % empty_iff
thf(fact_19_insert__absorb2, axiom,
    ((![X2 : nat, A2 : set_nat]: ((insert_nat @ X2 @ (insert_nat @ X2 @ A2)) = (insert_nat @ X2 @ A2))))). % insert_absorb2
thf(fact_20_insert__iff, axiom,
    ((![A : nat, B : nat, A2 : set_nat]: ((member_nat @ A @ (insert_nat @ B @ A2)) = (((A = B)) | ((member_nat @ A @ A2))))))). % insert_iff
thf(fact_21_insertCI, axiom,
    ((![A : nat, B2 : set_nat, B : nat]: (((~ ((member_nat @ A @ B2))) => (A = B)) => (member_nat @ A @ (insert_nat @ B @ B2)))))). % insertCI
thf(fact_22_semiring__norm_I90_J, axiom,
    ((![M : num, N : num]: (((bit1 @ M) = (bit1 @ N)) = (M = N))))). % semiring_norm(90)
thf(fact_23_semiring__norm_I83_J, axiom,
    ((![N : num]: (~ ((one = (bit0 @ N))))))). % semiring_norm(83)
thf(fact_24_ex__in__conv, axiom,
    ((![A2 : set_nat]: ((?[X : nat]: (member_nat @ X @ A2)) = (~ ((A2 = bot_bot_set_nat))))))). % ex_in_conv
thf(fact_25_equals0I, axiom,
    ((![A2 : set_nat]: ((![Y : nat]: (~ ((member_nat @ Y @ A2)))) => (A2 = bot_bot_set_nat))))). % equals0I
thf(fact_26_equals0D, axiom,
    ((![A2 : set_nat, A : nat]: ((A2 = bot_bot_set_nat) => (~ ((member_nat @ A @ A2))))))). % equals0D
thf(fact_27_emptyE, axiom,
    ((![A : nat]: (~ ((member_nat @ A @ bot_bot_set_nat)))))). % emptyE
thf(fact_28_mk__disjoint__insert, axiom,
    ((![A : nat, A2 : set_nat]: ((member_nat @ A @ A2) => (?[B3 : set_nat]: ((A2 = (insert_nat @ A @ B3)) & (~ ((member_nat @ A @ B3))))))))). % mk_disjoint_insert
thf(fact_29_insert__commute, axiom,
    ((![X2 : nat, Y2 : nat, A2 : set_nat]: ((insert_nat @ X2 @ (insert_nat @ Y2 @ A2)) = (insert_nat @ Y2 @ (insert_nat @ X2 @ A2)))))). % insert_commute
thf(fact_30_insert__eq__iff, axiom,
    ((![A : nat, A2 : set_nat, B : nat, B2 : set_nat]: ((~ ((member_nat @ A @ A2))) => ((~ ((member_nat @ B @ B2))) => (((insert_nat @ A @ A2) = (insert_nat @ B @ B2)) = (((((A = B)) => ((A2 = B2)))) & ((((~ ((A = B)))) => ((?[C2 : set_nat]: (((A2 = (insert_nat @ B @ C2))) & ((((~ ((member_nat @ B @ C2)))) & ((((B2 = (insert_nat @ A @ C2))) & ((~ ((member_nat @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_31_insert__absorb, axiom,
    ((![A : nat, A2 : set_nat]: ((member_nat @ A @ A2) => ((insert_nat @ A @ A2) = A2))))). % insert_absorb
thf(fact_32_insert__ident, axiom,
    ((![X2 : nat, A2 : set_nat, B2 : set_nat]: ((~ ((member_nat @ X2 @ A2))) => ((~ ((member_nat @ X2 @ B2))) => (((insert_nat @ X2 @ A2) = (insert_nat @ X2 @ B2)) = (A2 = B2))))))). % insert_ident
thf(fact_33_Set_Oset__insert, axiom,
    ((![X2 : nat, A2 : set_nat]: ((member_nat @ X2 @ A2) => (~ ((![B3 : set_nat]: ((A2 = (insert_nat @ X2 @ B3)) => (member_nat @ X2 @ B3))))))))). % Set.set_insert
thf(fact_34_insertI2, axiom,
    ((![A : nat, B2 : set_nat, B : nat]: ((member_nat @ A @ B2) => (member_nat @ A @ (insert_nat @ B @ B2)))))). % insertI2
thf(fact_35_insertI1, axiom,
    ((![A : nat, B2 : set_nat]: (member_nat @ A @ (insert_nat @ A @ B2))))). % insertI1
thf(fact_36_insertE, axiom,
    ((![A : nat, B : nat, A2 : set_nat]: ((member_nat @ A @ (insert_nat @ B @ A2)) => ((~ ((A = B))) => (member_nat @ A @ A2)))))). % insertE
thf(fact_37_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N))))))). % zero_neq_numeral
thf(fact_38_singleton__inject, axiom,
    ((![A : nat, B : nat]: (((insert_nat @ A @ bot_bot_set_nat) = (insert_nat @ B @ bot_bot_set_nat)) => (A = B))))). % singleton_inject
thf(fact_39_insert__not__empty, axiom,
    ((![A : nat, A2 : set_nat]: (~ (((insert_nat @ A @ A2) = bot_bot_set_nat)))))). % insert_not_empty
thf(fact_40_doubleton__eq__iff, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: (((insert_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)) = (insert_nat @ C @ (insert_nat @ D @ bot_bot_set_nat))) = (((((A = C)) & ((B = D)))) | ((((A = D)) & ((B = C))))))))). % doubleton_eq_iff
thf(fact_41_singleton__iff, axiom,
    ((![B : nat, A : nat]: ((member_nat @ B @ (insert_nat @ A @ bot_bot_set_nat)) = (B = A))))). % singleton_iff
thf(fact_42_singletonD, axiom,
    ((![B : nat, A : nat]: ((member_nat @ B @ (insert_nat @ A @ bot_bot_set_nat)) => (B = A))))). % singletonD
thf(fact_43_numeral__One, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numeral_One
thf(fact_44_num_Oexhaust, axiom,
    ((![Y2 : num]: ((~ ((Y2 = one))) => ((![X22 : num]: (~ ((Y2 = (bit0 @ X22))))) => (~ ((![X3 : num]: (~ ((Y2 = (bit1 @ X3)))))))))))). % num.exhaust
thf(fact_45_num_Oinduct, axiom,
    ((![P : num > $o, Num : num]: ((P @ one) => ((![X4 : num]: ((P @ X4) => (P @ (bit0 @ X4)))) => ((![X4 : num]: ((P @ X4) => (P @ (bit1 @ X4)))) => (P @ Num))))))). % num.induct
thf(fact_46_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)
thf(fact_47_atLeastLessThan0, axiom,
    ((![M : nat]: ((set_or562006527an_nat @ M @ zero_zero_nat) = bot_bot_set_nat)))). % atLeastLessThan0
thf(fact_48_numeral__1__eq__Suc__0, axiom,
    (((numeral_numeral_nat @ one) = (suc @ zero_zero_nat)))). % numeral_1_eq_Suc_0
thf(fact_49_eval__nat__numeral_I3_J, axiom,
    ((![N : num]: ((numeral_numeral_nat @ (bit1 @ N)) = (suc @ (numeral_numeral_nat @ (bit0 @ N))))))). % eval_nat_numeral(3)
thf(fact_50_atLeast0__lessThan__Suc, axiom,
    ((![N : nat]: ((set_or562006527an_nat @ zero_zero_nat @ (suc @ N)) = (insert_nat @ N @ (set_or562006527an_nat @ zero_zero_nat @ N)))))). % atLeast0_lessThan_Suc
thf(fact_51_One__nat__def, axiom,
    ((one_one_nat = (suc @ zero_zero_nat)))). % One_nat_def
thf(fact_52_verit__eq__simplify_I9_J, axiom,
    ((![X32 : num, Y3 : num]: (((bit1 @ X32) = (bit1 @ Y3)) = (X32 = Y3))))). % verit_eq_simplify(9)
thf(fact_53_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_54_nat_Oinject, axiom,
    ((![X23 : nat, Y22 : nat]: (((suc @ X23) = (suc @ Y22)) = (X23 = Y22))))). % nat.inject
thf(fact_55_the__elem__eq, axiom,
    ((![X2 : nat]: ((the_elem_nat @ (insert_nat @ X2 @ bot_bot_set_nat)) = X2)))). % the_elem_eq
thf(fact_56_verit__eq__simplify_I8_J, axiom,
    ((![X23 : num, Y22 : num]: (((bit0 @ X23) = (bit0 @ Y22)) = (X23 = Y22))))). % verit_eq_simplify(8)
thf(fact_57_bot__nat__def, axiom,
    ((bot_bot_nat = zero_zero_nat))). % bot_nat_def
thf(fact_58_bot__set__def, axiom,
    ((bot_bot_set_nat = (collect_nat @ bot_bot_nat_o)))). % bot_set_def
thf(fact_59_Suc__inject, axiom,
    ((![X2 : nat, Y2 : nat]: (((suc @ X2) = (suc @ Y2)) => (X2 = Y2))))). % Suc_inject
thf(fact_60_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_61_verit__eq__simplify_I10_J, axiom,
    ((![X23 : num]: (~ ((one = (bit0 @ X23))))))). % verit_eq_simplify(10)
thf(fact_62_nat_Odistinct_I1_J, axiom,
    ((![X23 : nat]: (~ ((zero_zero_nat = (suc @ X23))))))). % nat.distinct(1)
thf(fact_63_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_64_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_65_nat_OdiscI, axiom,
    ((![Nat : nat, X23 : nat]: ((Nat = (suc @ X23)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_66_nat__induct, axiom,
    ((![P : nat > $o, N : nat]: ((P @ zero_zero_nat) => ((![N2 : nat]: ((P @ N2) => (P @ (suc @ N2)))) => (P @ N)))))). % nat_induct
thf(fact_67_diff__induct, axiom,
    ((![P : nat > nat > $o, M : nat, N : nat]: ((![X4 : nat]: (P @ X4 @ zero_zero_nat)) => ((![Y : nat]: (P @ zero_zero_nat @ (suc @ Y))) => ((![X4 : nat, Y : nat]: ((P @ X4 @ Y) => (P @ (suc @ X4) @ (suc @ Y)))) => (P @ M @ N))))))). % diff_induct
thf(fact_68_zero__induct, axiom,
    ((![P : nat > $o, K : nat]: ((P @ K) => ((![N2 : nat]: ((P @ (suc @ N2)) => (P @ N2))) => (P @ zero_zero_nat)))))). % zero_induct
thf(fact_69_Suc__neq__Zero, axiom,
    ((![M : nat]: (~ (((suc @ M) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_70_Zero__neq__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_neq_Suc
thf(fact_71_Zero__not__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_not_Suc
thf(fact_72_old_Onat_Oexhaust, axiom,
    ((![Y2 : nat]: ((~ ((Y2 = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y2 = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_73_old_Onat_Oinducts, axiom,
    ((![P : nat > $o, Nat : nat]: ((P @ zero_zero_nat) => ((![Nat3 : nat]: ((P @ Nat3) => (P @ (suc @ Nat3)))) => (P @ Nat)))))). % old.nat.inducts
thf(fact_74_not0__implies__Suc, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (?[M2 : nat]: (N = (suc @ M2))))))). % not0_implies_Suc
thf(fact_75_verit__eq__simplify_I14_J, axiom,
    ((![X23 : num, X32 : num]: (~ (((bit0 @ X23) = (bit1 @ X32))))))). % verit_eq_simplify(14)
thf(fact_76_verit__eq__simplify_I12_J, axiom,
    ((![X32 : num]: (~ ((one = (bit1 @ X32))))))). % verit_eq_simplify(12)
thf(fact_77_is__singleton__the__elem, axiom,
    ((is_singleton_nat = (^[A3 : set_nat]: (A3 = (insert_nat @ (the_elem_nat @ A3) @ bot_bot_set_nat)))))). % is_singleton_the_elem
thf(fact_78_is__singletonI, axiom,
    ((![X2 : nat]: (is_singleton_nat @ (insert_nat @ X2 @ bot_bot_set_nat))))). % is_singletonI
thf(fact_79_is__singletonI_H, axiom,
    ((![A2 : set_nat]: ((~ ((A2 = bot_bot_set_nat))) => ((![X4 : nat, Y : nat]: ((member_nat @ X4 @ A2) => ((member_nat @ Y @ A2) => (X4 = Y)))) => (is_singleton_nat @ A2)))))). % is_singletonI'
thf(fact_80_zero__reorient, axiom,
    ((![X2 : nat]: ((zero_zero_nat = X2) = (X2 = zero_zero_nat))))). % zero_reorient
thf(fact_81_one__reorient, axiom,
    ((![X2 : nat]: ((one_one_nat = X2) = (X2 = one_one_nat))))). % one_reorient
thf(fact_82_is__singleton__def, axiom,
    ((is_singleton_nat = (^[A3 : set_nat]: (?[X : nat]: (A3 = (insert_nat @ X @ bot_bot_set_nat))))))). % is_singleton_def
thf(fact_83_is__singletonE, axiom,
    ((![A2 : set_nat]: ((is_singleton_nat @ A2) => (~ ((![X4 : nat]: (~ ((A2 = (insert_nat @ X4 @ bot_bot_set_nat))))))))))). % is_singletonE
thf(fact_84_bot__empty__eq, axiom,
    ((bot_bot_nat_o = (^[X : nat]: (member_nat @ X @ bot_bot_set_nat))))). % bot_empty_eq
thf(fact_85_Collect__empty__eq__bot, axiom,
    ((![P : nat > $o]: (((collect_nat @ P) = bot_bot_set_nat) = (P = bot_bot_nat_o))))). % Collect_empty_eq_bot
thf(fact_86_exists__least__lemma, axiom,
    ((![P : nat > $o]: ((~ ((P @ zero_zero_nat))) => ((?[X_1 : nat]: (P @ X_1)) => (?[N2 : nat]: ((~ ((P @ N2))) & (P @ (suc @ N2))))))))). % exists_least_lemma
thf(fact_87_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one

% Conjectures (1)
thf(conj_0, conjecture,
    (((set_or562006527an_nat @ zero_zero_nat @ (suc @ (suc @ (suc @ (suc @ zero_zero_nat))))) = (insert_nat @ zero_zero_nat @ (insert_nat @ one_one_nat @ (insert_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (insert_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ bot_bot_set_nat))))))).
