%   ORIGINAL: h4/DeepSyntax/in__bset_c9
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/bool/RIGHT__EXISTS__AND__THM: !Q P. (?x. P /\ Q x) <=> P /\ (?x. Q x)
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm: h4/pred__set/IN__UNION: !x t s. h4/bool/IN x (h4/pred__set/UNION s t) <=> h4/bool/IN x s \/ h4/bool/IN x t
% Assm: h4/pred__set/IN__SING: !y x. h4/bool/IN x (h4/pred__set/INSERT y h4/pred__set/EMPTY) <=> x = y
% Assm: h4/DeepSyntax/Bset__def_c0: !pos f2 f1. h4/DeepSyntax/Bset pos (h4/DeepSyntax/Conjn f1 f2) = h4/pred__set/UNION (h4/DeepSyntax/Bset pos f1) (h4/DeepSyntax/Bset pos f2)
% Assm: h4/DeepSyntax/Bset__def_c1: !pos f2 f1. h4/DeepSyntax/Bset pos (h4/DeepSyntax/Disjn f1 f2) = h4/pred__set/UNION (h4/DeepSyntax/Bset pos f1) (h4/DeepSyntax/Bset pos f2)
% Assm: h4/DeepSyntax/Bset__def_c2: !pos f. h4/DeepSyntax/Bset pos (h4/DeepSyntax/Negn f) = h4/DeepSyntax/Bset (~pos) f
% Assm: h4/DeepSyntax/Bset__def_c3: !pos b. h4/DeepSyntax/Bset pos (h4/DeepSyntax/UnrelatedBool b) = h4/pred__set/EMPTY
% Assm: h4/DeepSyntax/Bset__def_c4: !pos i. h4/DeepSyntax/Bset pos (h4/DeepSyntax/xLT i) = h4/bool/COND pos h4/pred__set/EMPTY (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) h4/pred__set/EMPTY)
% Assm: h4/DeepSyntax/Bset__def_c5: !pos i. h4/DeepSyntax/Bset pos (h4/DeepSyntax/LTx i) = h4/bool/COND pos (h4/pred__set/INSERT i h4/pred__set/EMPTY) h4/pred__set/EMPTY
% Assm: h4/DeepSyntax/Bset__def_c6: !pos i. h4/DeepSyntax/Bset pos (h4/DeepSyntax/xEQ i) = h4/bool/COND pos (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) h4/pred__set/EMPTY) (h4/pred__set/INSERT i h4/pred__set/EMPTY)
% Assm: h4/DeepSyntax/Bset__def_c7: !pos i2 i1. h4/DeepSyntax/Bset pos (h4/DeepSyntax/xDivided i1 i2) = h4/pred__set/EMPTY
% Goal: !i P. (?b. h4/bool/IN b (h4/DeepSyntax/Bset T (h4/DeepSyntax/xEQ i)) /\ P b) <=> P (h4/integer/int__add i (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. P /\ happ Q x) <=> P /\ (?x. happ Q x)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_INu_u_UNION]: !x t s. h4/bool/IN x (h4/pred__set/UNION s t) <=> h4/bool/IN x s \/ h4/bool/IN x t
% Assm [h4s_predu_u_sets_INu_u_SING]: !y x. h4/bool/IN x (h4/pred__set/INSERT y h4/pred__set/EMPTY) <=> x = y
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c0]: !pos f2 f1. h4/DeepSyntax/Bset pos (h4/DeepSyntax/Conjn f1 f2) = h4/pred__set/UNION (h4/DeepSyntax/Bset pos f1) (h4/DeepSyntax/Bset pos f2)
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c1]: !pos f2 f1. h4/DeepSyntax/Bset pos (h4/DeepSyntax/Disjn f1 f2) = h4/pred__set/UNION (h4/DeepSyntax/Bset pos f1) (h4/DeepSyntax/Bset pos f2)
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c2]: !pos f. ?v. (v <=> ~pos) /\ h4/DeepSyntax/Bset pos (h4/DeepSyntax/Negn f) = h4/DeepSyntax/Bset v f
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c3]: !pos b. h4/DeepSyntax/Bset pos (h4/DeepSyntax/UnrelatedBool b) = h4/pred__set/EMPTY
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c4]: !pos i. h4/DeepSyntax/Bset pos (h4/DeepSyntax/xLT i) = h4/bool/COND pos h4/pred__set/EMPTY (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) h4/pred__set/EMPTY)
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c5]: !pos i. h4/DeepSyntax/Bset pos (h4/DeepSyntax/LTx i) = h4/bool/COND pos (h4/pred__set/INSERT i h4/pred__set/EMPTY) h4/pred__set/EMPTY
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c6]: !pos i. h4/DeepSyntax/Bset pos (h4/DeepSyntax/xEQ i) = h4/bool/COND pos (h4/pred__set/INSERT (h4/integer/int__add i (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) h4/pred__set/EMPTY) (h4/pred__set/INSERT i h4/pred__set/EMPTY)
% Assm [h4s_DeepSyntaxs_Bsetu_u_defu_c7]: !pos i2 i1. h4/DeepSyntax/Bset pos (h4/DeepSyntax/xDivided i1 i2) = h4/pred__set/EMPTY
% Goal: !i P. (?b. h4/bool/IN b (h4/DeepSyntax/Bset T (h4/DeepSyntax/xEQ i)) /\ happ P b) <=> happ P (h4/integer/int__add i (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q350608,TV_Q350604]: ![V_f, V_g]: (![V_x]: s(TV_Q350604,happ(s(t_fun(TV_Q350608,TV_Q350604),V_f),s(TV_Q350608,V_x))) = s(TV_Q350604,happ(s(t_fun(TV_Q350608,TV_Q350604),V_g),s(TV_Q350608,V_x))) => s(t_fun(TV_Q350608,TV_Q350604),V_f) = s(t_fun(TV_Q350608,TV_Q350604),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_NOTu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ![V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_EXISTSu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))))).
fof(ah4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (p(s(t_bool,V_P)) & ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_predu_u_sets_INu_u_UNION, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_predu_u_sets_INu_u_SING, axiom, ![TV_u_27a]: ![V_y, V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c0, axiom, ![V_pos, V_f2, V_f1]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_conjn(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_union(s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2)))))).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c1, axiom, ![V_pos, V_f2, V_f1]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_disjn(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_union(s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f1))),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f2)))))).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c2, axiom, ![V_pos, V_f]: ?[V_v]: ((p(s(t_bool,V_v)) <=> ~ (p(s(t_bool,V_pos)))) & s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_negn(s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_v),s(t_h4s_DeepSyntaxs_deepu_u_form,V_f))))).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c3, axiom, ![V_pos, V_b]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_unrelatedbool(s(t_bool,V_b))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c4, axiom, ![V_pos, V_i]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_xlt(s(t_h4s_integers_int,V_i))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_bools_cond(s(t_bool,V_pos),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_insert(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c5, axiom, ![V_pos, V_i]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_ltx(s(t_h4s_integers_int,V_i))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_bools_cond(s(t_bool,V_pos),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_insert(s(t_h4s_integers_int,V_i),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty))),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty)))).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c6, axiom, ![V_pos, V_i]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_xeq(s(t_h4s_integers_int,V_i))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_bools_cond(s(t_bool,V_pos),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_insert(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty))),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_insert(s(t_h4s_integers_int,V_i),s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_DeepSyntaxs_Bsetu_u_defu_c7, axiom, ![V_pos, V_i2, V_i1]: s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,V_pos),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_xdivided(s(t_h4s_integers_int,V_i1),s(t_h4s_integers_int,V_i2))))) = s(t_fun(t_h4s_integers_int,t_bool),h4s_predu_u_sets_empty)).
fof(ch4s_DeepSyntaxs_inu_u_bsetu_c9, conjecture, ![V_i, V_P]: (?[V_b]: (p(s(t_bool,h4s_bools_in(s(t_h4s_integers_int,V_b),s(t_fun(t_h4s_integers_int,t_bool),h4s_deepsyntaxs_bset(s(t_bool,t),s(t_h4s_DeepSyntaxs_deepu_u_form,h4s_deepsyntaxs_xeq(s(t_h4s_integers_int,V_i)))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,V_b))))) <=> p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),V_P),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))).
