%   ORIGINAL: h4/ringNorm/polynom__distinct_c1
% 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/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/ringNorm/polynom__11_c2: !a1_27 a1 a0_27 a0. h4/ringNorm/Pplus a0 a1 = h4/ringNorm/Pplus a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/ringNorm/polynom__size__def_c2: !f a1 a0. h4/ringNorm/polynom__size f (h4/ringNorm/Pplus a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/ringNorm/polynom__size f a0) (h4/ringNorm/polynom__size f a1))
% Assm: h4/ringNorm/Pplus0: h4/ringNorm/Pplus = h4/ringNorm/_20_40ind__typeringNorm2
% Assm: h4/ringNorm/Pvar0: h4/ringNorm/Pvar = h4/ringNorm/_20_40ind__typeringNorm0
% Assm: h4/ringNorm/datatype__polynom: !polynom. h4/bool/DATATYPE (polynom h4/ringNorm/Pvar h4/ringNorm/Pconst h4/ringNorm/Pplus h4/ringNorm/Pmult h4/ringNorm/Popp)
% Assm: h4/ringNorm/hidden____20__40ind____typeringNorm4____def: h4/ringNorm/_20_40ind__typeringNorm4 = (\a. h4/ringNorm/_20_40ind__typeringNorm5 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/ringNorm/_20_40ind__typeringNorm6 a)))
% Assm: h4/ringNorm/polynom__repfns_c0: !a. h4/ringNorm/_20_40ind__typeringNorm5 (h4/ringNorm/_20_40ind__typeringNorm6 a) = a
% Assm: h4/ringNorm/hidden____20__40ind____typeringNorm2____def: h4/ringNorm/_20_40ind__typeringNorm2 = (\a0 a1. h4/ringNorm/_20_40ind__typeringNorm5 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/ringNorm/_20_40ind__typeringNorm6 a0) (h4/ringNorm/_20_40ind__typeringNorm6 a1)))
% Assm: h4/ringNorm/hidden____20__40ind____typeringNorm3____def: h4/ringNorm/_20_40ind__typeringNorm3 = (\a0 a1. h4/ringNorm/_20_40ind__typeringNorm5 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/ringNorm/_20_40ind__typeringNorm6 a0) (h4/ringNorm/_20_40ind__typeringNorm6 a1)))
% Assm: h4/ringNorm/polynom__distinct_c0: !a_27 a. ~(h4/ringNorm/Pvar a = h4/ringNorm/Pconst a_27)
% Assm: h4/ringNorm/polynom__11_c0: !a_27 a. h4/ringNorm/Pvar a = h4/ringNorm/Pvar a_27 <=> a = a_27
% Assm: h4/ringNorm/polynom__case__def_c0: !f4 f3 f2 f1 f a. h4/ringNorm/polynom__CASE (h4/ringNorm/Pvar a) f f1 f2 f3 f4 = f a
% Assm: h4/ringNorm/polynom__size__def_c0: !f a. h4/ringNorm/polynom__size f (h4/ringNorm/Pvar a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/quote/index__size a)
% Assm: h4/ringNorm/polynom__repfns_c1: !r. (\a0_27. !_27polynom_27. (!a0_270. (?a. a0_270 = (\a0. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 h4/bool/ARB) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a0) (\n. h4/ind__type/BOTTOM)) a) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27polynom_27 a0 /\ _27polynom_27 a1) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27polynom_27 a0 /\ _27polynom_27 a1) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) a /\ _27polynom_27 a) ==> _27polynom_27 a0_270) ==> _27polynom_27 a0_27) r <=> h4/ringNorm/_20_40ind__typeringNorm6 (h4/ringNorm/_20_40ind__typeringNorm5 r) = r
% Assm: h4/ringNorm/hidden____20__40ind____typeringNorm0____def: h4/ringNorm/_20_40ind__typeringNorm0 = (\a. h4/ringNorm/_20_40ind__typeringNorm5 ((\a0. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 h4/bool/ARB) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/ringNorm/hidden____20__40ind____typeringNorm1____def: h4/ringNorm/_20_40ind__typeringNorm1 = (\a. h4/ringNorm/_20_40ind__typeringNorm5 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a0) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/ringNorm/Pmult0: h4/ringNorm/Pmult = h4/ringNorm/_20_40ind__typeringNorm3
% Assm: h4/ringNorm/Pconst0: h4/ringNorm/Pconst = h4/ringNorm/_20_40ind__typeringNorm1
% Assm: h4/ringNorm/Popp0: h4/ringNorm/Popp = h4/ringNorm/_20_40ind__typeringNorm4
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/ringNorm/polynom__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\a0_27. !_27polynom_27. (!a0_270. (?a. a0_270 = (\a0. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 h4/bool/ARB) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a0) (\n. h4/ind__type/BOTTOM)) a) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27polynom_27 a0 /\ _27polynom_27 a1) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27polynom_27 a0 /\ _27polynom_27 a1) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) a /\ _27polynom_27 a) ==> _27polynom_27 a0_270) ==> _27polynom_27 a0_27) rep
% Assm: h4/bool/ABS__REP__THM: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. abs (rep a) = a) /\ (!r. P r <=> rep (abs r) = r))
% Assm: h4/ringNorm/polynom__case__def_c2: !f4 f3 f2 f1 f a1 a0. h4/ringNorm/polynom__CASE (h4/ringNorm/Pplus a0 a1) f f1 f2 f3 f4 = f2 a0 a1
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/ringNorm/polynom__11_c3: !a1_27 a1 a0_27 a0. h4/ringNorm/Pmult a0 a1 = h4/ringNorm/Pmult a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/ringNorm/polynom__size__def_c3: !f a1 a0. h4/ringNorm/polynom__size f (h4/ringNorm/Pmult a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/ringNorm/polynom__size f a0) (h4/ringNorm/polynom__size f a1))
% Assm: h4/ringNorm/polynom__size__def_c4: !f a. h4/ringNorm/polynom__size f (h4/ringNorm/Popp a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/ringNorm/polynom__size f a)
% Assm: h4/ringNorm/polynom__11_c4: !a_27 a. h4/ringNorm/Popp a = h4/ringNorm/Popp a_27 <=> a = a_27
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/ringNorm/polynom__case__def_c1: !f4 f3 f2 f1 f a. h4/ringNorm/polynom__CASE (h4/ringNorm/Pconst a) f f1 f2 f3 f4 = f1 a
% Assm: h4/ringNorm/polynom__case__def_c4: !f4 f3 f2 f1 f a. h4/ringNorm/polynom__CASE (h4/ringNorm/Popp a) f f1 f2 f3 f4 = f4 a
% Assm: h4/ringNorm/polynom__case__def_c3: !f4 f3 f2 f1 f a1 a0. h4/ringNorm/polynom__CASE (h4/ringNorm/Pmult a0 a1) f f1 f2 f3 f4 = f3 a0 a1
% Assm: h4/ringNorm/polynom__size__def_c1: !f a. h4/ringNorm/polynom__size f (h4/ringNorm/Pconst a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (f a)
% Assm: h4/ringNorm/polynom__11_c1: !a_27 a. h4/ringNorm/Pconst a = h4/ringNorm/Pconst a_27 <=> a = a_27
% Assm: h4/canonical/spolynom__distinct_c0: !a_27 a. ~(h4/canonical/SPvar a = h4/canonical/SPconst a_27)
% Assm: h4/quote/index__distinct_c0: !a_27 a. ~(h4/quote/Left__idx a = h4/quote/Right__idx a_27)
% Assm: h4/canonical/spolynom__distinct_c1: !a1 a0 a. ~(h4/canonical/SPvar a = h4/canonical/SPplus a0 a1)
% Assm: h4/canonical/spolynom__distinct_c2: !a1 a0 a. ~(h4/canonical/SPvar a = h4/canonical/SPmult a0 a1)
% Assm: h4/quote/index__distinct_c1: !a. ~(h4/quote/Left__idx a = h4/quote/End__idx)
% Assm: h4/quote/index__distinct_c2: !a. ~(h4/quote/Right__idx a = h4/quote/End__idx)
% Assm: h4/quote/index__Axiom: !f2 f1 f0. ?fn. (!a. fn (h4/quote/Left__idx a) = f0 a (fn a)) /\ (!a. fn (h4/quote/Right__idx a) = f1 a (fn a)) /\ fn h4/quote/End__idx = f2
% Assm: h4/quote/index__11_c0: !a_27 a. h4/quote/Left__idx a = h4/quote/Left__idx a_27 <=> a = a_27
% Assm: h4/quote/index__compare__def_c5: !n_27 m_27. h4/quote/index__compare (h4/quote/Left__idx n_27) (h4/quote/Left__idx m_27) = h4/quote/index__compare n_27 m_27
% Assm: h4/quote/hidden____20__40ind____typequote1____def: h4/quote/_20_40ind__typequote1 = (\a. h4/quote/_20_40ind__typequote3 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/quote/_20_40ind__typequote4 a)))
% Assm: h4/quote/hidden____20__40ind____typequote0____def: h4/quote/_20_40ind__typequote0 = (\a. h4/quote/_20_40ind__typequote3 ((\a0. h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/quote/_20_40ind__typequote4 a)))
% Assm: h4/quote/index__repfns_c1: !r. (\a0. !_27index_27. (!a00. (?a. a00 = (\a1. h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (h4/ind__type/FCONS a1 (\n. h4/ind__type/BOTTOM))) a /\ _27index_27 a) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a1 (\n. h4/ind__type/BOTTOM))) a /\ _27index_27 a) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (\n. h4/ind__type/BOTTOM) ==> _27index_27 a00) ==> _27index_27 a0) r <=> h4/quote/_20_40ind__typequote4 (h4/quote/_20_40ind__typequote3 r) = r
% Assm: h4/quote/index__repfns_c0: !a. h4/quote/_20_40ind__typequote3 (h4/quote/_20_40ind__typequote4 a) = a
% Assm: h4/quote/Left__idx0: h4/quote/Left__idx = h4/quote/_20_40ind__typequote0
% Assm: h4/quote/hidden____20__40ind____typequote2____def: h4/quote/_20_40ind__typequote2 = h4/quote/_20_40ind__typequote3 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/quote/Right__idx0: h4/quote/Right__idx = h4/quote/_20_40ind__typequote1
% Assm: h4/quote/End__idx0: h4/quote/End__idx = h4/quote/_20_40ind__typequote2
% Assm: h4/canonical/SPmult0: h4/canonical/SPmult = h4/canonical/_20_40ind__typecanonical8
% Assm: h4/canonical/hidden____20__40ind____typecanonical8____def: h4/canonical/_20_40ind__typecanonical8 = (\a0 a1. h4/canonical/_20_40ind__typecanonical9 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/canonical/_20_40ind__typecanonical10 a0) (h4/canonical/_20_40ind__typecanonical10 a1)))
% Assm: h4/canonical/SPvar0: h4/canonical/SPvar = h4/canonical/_20_40ind__typecanonical5
% Assm: h4/canonical/SPconst0: h4/canonical/SPconst = h4/canonical/_20_40ind__typecanonical6
% Assm: h4/canonical/hidden____20__40ind____typecanonical6____def: h4/canonical/_20_40ind__typecanonical6 = (\a. h4/canonical/_20_40ind__typecanonical9 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a0) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/canonical/SPplus0: h4/canonical/SPplus = h4/canonical/_20_40ind__typecanonical7
% Assm: h4/canonical/hidden____20__40ind____typecanonical7____def: h4/canonical/_20_40ind__typecanonical7 = (\a0 a1. h4/canonical/_20_40ind__typecanonical9 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/canonical/_20_40ind__typecanonical10 a0) (h4/canonical/_20_40ind__typecanonical10 a1)))
% Assm: h4/canonical/hidden____20__40ind____typecanonical5____def: h4/canonical/_20_40ind__typecanonical5 = (\a. h4/canonical/_20_40ind__typecanonical9 ((\a0. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 h4/bool/ARB) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/canonical/spolynom__repfns_c0: !a. h4/canonical/_20_40ind__typecanonical9 (h4/canonical/_20_40ind__typecanonical10 a) = a
% Assm: h4/canonical/spolynom__repfns_c1: !r. (\a0_27. !_27spolynom_27. (!a0_270. (?a. a0_270 = (\a0. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 h4/bool/ARB) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a0) (\n. h4/ind__type/BOTTOM)) a) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27spolynom_27 a0 /\ _27spolynom_27 a1) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27spolynom_27 a0 /\ _27spolynom_27 a1) ==> _27spolynom_27 a0_270) ==> _27spolynom_27 a0_27) r <=> h4/canonical/_20_40ind__typecanonical10 (h4/canonical/_20_40ind__typecanonical9 r) = r
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/quote/index__compare__curried__def: !x1 x. h4/quote/index__compare x x1 = h4/quote/index__compare__tupled (h4/pair/_2C x x1)
% Assm: h4/quote/index__compare__tupled__primitive__def: h4/quote/index__compare__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!m_27 n_27. R (h4/pair/_2C n_27 m_27) (h4/pair/_2C (h4/quote/Left__idx n_27) (h4/quote/Left__idx m_27))) /\ (!m_27 n_27. R (h4/pair/_2C n_27 m_27) (h4/pair/_2C (h4/quote/Right__idx n_27) (h4/quote/Right__idx m_27))))) (\index__compare__tupled a. h4/pair/pair__CASE a (\v v1. h4/quote/index__CASE v (\n_27. h4/quote/index__CASE v1 (\m_27. h4/combin/I (index__compare__tupled (h4/pair/_2C n_27 m_27))) (\m_27_27. h4/combin/I h4/prelim/LESS) (h4/combin/I h4/prelim/GREATER)) (\n_27_27. h4/quote/index__CASE v1 (\m_27_27_27_27. h4/combin/I h4/prelim/GREATER) (\m_27_27_27. h4/combin/I (index__compare__tupled (h4/pair/_2C n_27_27 m_27_27_27))) (h4/combin/I h4/prelim/GREATER)) (h4/quote/index__CASE v1 (\v12. h4/combin/I h4/prelim/LESS) (\v13. h4/combin/I h4/prelim/LESS) (h4/combin/I h4/prelim/EQUAL))))
% Assm: h4/quote/index__size__def_c1: !a. h4/quote/index__size (h4/quote/Right__idx a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/quote/index__size a)
% Assm: h4/quote/index__size__def_c0: !a. h4/quote/index__size (h4/quote/Left__idx a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/quote/index__size a)
% Assm: h4/quote/index__case__def_c1: !v f1 f a. h4/quote/index__CASE (h4/quote/Right__idx a) f f1 v = f1 a
% Assm: h4/quote/index__case__def_c2: !v f1 f. h4/quote/index__CASE h4/quote/End__idx f f1 v = v
% Assm: h4/quote/index__case__def_c0: !v f1 f a. h4/quote/index__CASE (h4/quote/Left__idx a) f f1 v = f a
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/numeral/numeral__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% 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__INV__IMP: !A. A ==> ~A ==> F
% Goal: !a1 a0 a. ~(h4/ringNorm/Pvar a = h4/ringNorm/Pplus a0 a1)
%   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_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_ringNorms_polynomu_u_11u_c2]: !a1_27 a1 a0_27 a0. happ (happ h4/ringNorm/Pplus a0) a1 = happ (happ h4/ringNorm/Pplus a0_27) a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_ringNorms_polynomu_u_sizeu_u_defu_c2]: !f a1 a0. h4/ringNorm/polynom__size f (happ (happ h4/ringNorm/Pplus a0) a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/ringNorm/polynom__size f a0) (h4/ringNorm/polynom__size f a1))
% Assm [h4s_ringNorms_Pplus0]: h4/ringNorm/Pplus = h4/ringNorm/_20_40ind__typeringNorm2
% Assm [h4s_ringNorms_Pvar0]: h4/ringNorm/Pvar = h4/ringNorm/_20_40ind__typeringNorm0
% Assm [h4s_ringNorms_datatypeu_u_polynom]: !polynom. h4/bool/DATATYPE (happ (happ (happ (happ (happ polynom h4/ringNorm/Pvar) h4/ringNorm/Pconst) h4/ringNorm/Pplus) h4/ringNorm/Pmult) h4/ringNorm/Popp)
% Assm [h4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm4u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/ringNorm/_20_40ind__typeringNorm4 x = h4/ringNorm/_20_40ind__typeringNorm5 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/ringNorm/_20_40ind__typeringNorm6 x) _0)))
% Assm [h4s_ringNorms_polynomu_u_repfnsu_c0]: !a. h4/ringNorm/_20_40ind__typeringNorm5 (h4/ringNorm/_20_40ind__typeringNorm6 a) = a
% Assm [h4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/ringNorm/_20_40ind__typeringNorm2 x) x' = h4/ringNorm/_20_40ind__typeringNorm5 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/ringNorm/_20_40ind__typeringNorm6 x) (h4/ind__type/FCONS (h4/ringNorm/_20_40ind__typeringNorm6 x') _0))))
% Assm [h4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm3u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/ringNorm/_20_40ind__typeringNorm3 x) x' = h4/ringNorm/_20_40ind__typeringNorm5 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/ringNorm/_20_40ind__typeringNorm6 x) (h4/ind__type/FCONS (h4/ringNorm/_20_40ind__typeringNorm6 x') _0))))
% Assm [h4s_ringNorms_polynomu_u_distinctu_c0]: !a_27 a. ~(happ h4/ringNorm/Pvar a = happ h4/ringNorm/Pconst a_27)
% Assm [h4s_ringNorms_polynomu_u_11u_c0]: !a_27 a. happ h4/ringNorm/Pvar a = happ h4/ringNorm/Pvar a_27 <=> a = a_27
% Assm [h4s_ringNorms_polynomu_u_caseu_u_defu_c0]: !f4 f3 f2 f1 f a. h4/ringNorm/polynom__CASE (happ h4/ringNorm/Pvar a) f f1 f2 f3 f4 = happ f a
% Assm [h4s_ringNorms_polynomu_u_sizeu_u_defu_c0]: !f a. h4/ringNorm/polynom__size f (happ h4/ringNorm/Pvar a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/quote/index__size a)
% Assm [h4s_ringNorms_polynomu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27polynom_27. (!a0_270. (?a. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a h4/bool/ARB) _0) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a) _0) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27polynom_27 a0 /\ happ _27polynom_27 a1) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27polynom_27 a0 /\ happ _27polynom_27 a1) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a _0) /\ happ _27polynom_27 a) ==> happ _27polynom_27 a0_270) ==> happ _27polynom_27 r) <=> h4/ringNorm/_20_40ind__typeringNorm6 (h4/ringNorm/_20_40ind__typeringNorm5 r) = r)
% Assm [h4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/ringNorm/_20_40ind__typeringNorm0 x = h4/ringNorm/_20_40ind__typeringNorm5 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C x h4/bool/ARB) _0))
% Assm [h4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/ringNorm/_20_40ind__typeringNorm1 x = h4/ringNorm/_20_40ind__typeringNorm5 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB x) _0))
% Assm [h4s_ringNorms_Pmult0]: h4/ringNorm/Pmult = h4/ringNorm/_20_40ind__typeringNorm3
% Assm [h4s_ringNorms_Pconst0]: h4/ringNorm/Pconst = h4/ringNorm/_20_40ind__typeringNorm1
% Assm [h4s_ringNorms_Popp0]: h4/ringNorm/Popp = h4/ringNorm/_20_40ind__typeringNorm4
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_ringNorms_polynomu_u_TYu_u_DEF]: !_1. (!n. happ _1 n = h4/ind__type/BOTTOM) ==> (!_0. (!a0_27. happ _0 a0_27 <=> (!_27polynom_27. (!a0_270. (?a. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a h4/bool/ARB) _1) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a) _1) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _1)) /\ happ _27polynom_27 a0 /\ happ _27polynom_27 a1) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _1)) /\ happ _27polynom_27 a0 /\ happ _27polynom_27 a1) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a _1) /\ happ _27polynom_27 a) ==> happ _27polynom_27 a0_270) ==> happ _27polynom_27 a0_27)) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep))
% Assm [h4s_bools_ABSu_u_REPu_u_THM]: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. happ abs (happ rep a) = a) /\ (!r. happ P r <=> happ rep (happ abs r) = r))
% Assm [h4s_ringNorms_polynomu_u_caseu_u_defu_c2]: !f4 f3 f2 f1 f a1 a0. h4/ringNorm/polynom__CASE (happ (happ h4/ringNorm/Pplus a0) a1) f f1 f2 f3 f4 = happ (happ f2 a0) a1
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_ringNorms_polynomu_u_11u_c3]: !a1_27 a1 a0_27 a0. happ (happ h4/ringNorm/Pmult a0) a1 = happ (happ h4/ringNorm/Pmult a0_27) a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_ringNorms_polynomu_u_sizeu_u_defu_c3]: !f a1 a0. h4/ringNorm/polynom__size f (happ (happ h4/ringNorm/Pmult a0) a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/ringNorm/polynom__size f a0) (h4/ringNorm/polynom__size f a1))
% Assm [h4s_ringNorms_polynomu_u_sizeu_u_defu_c4]: !f a. h4/ringNorm/polynom__size f (happ h4/ringNorm/Popp a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/ringNorm/polynom__size f a)
% Assm [h4s_ringNorms_polynomu_u_11u_c4]: !a_27 a. happ h4/ringNorm/Popp a = happ h4/ringNorm/Popp a_27 <=> a = a_27
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_ringNorms_polynomu_u_caseu_u_defu_c1]: !f4 f3 f2 f1 f a. h4/ringNorm/polynom__CASE (happ h4/ringNorm/Pconst a) f f1 f2 f3 f4 = happ f1 a
% Assm [h4s_ringNorms_polynomu_u_caseu_u_defu_c4]: !f4 f3 f2 f1 f a. h4/ringNorm/polynom__CASE (happ h4/ringNorm/Popp a) f f1 f2 f3 f4 = happ f4 a
% Assm [h4s_ringNorms_polynomu_u_caseu_u_defu_c3]: !f4 f3 f2 f1 f a1 a0. h4/ringNorm/polynom__CASE (happ (happ h4/ringNorm/Pmult a0) a1) f f1 f2 f3 f4 = happ (happ f3 a0) a1
% Assm [h4s_ringNorms_polynomu_u_sizeu_u_defu_c1]: !f a. h4/ringNorm/polynom__size f (happ h4/ringNorm/Pconst a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (happ f a)
% Assm [h4s_ringNorms_polynomu_u_11u_c1]: !a_27 a. happ h4/ringNorm/Pconst a = happ h4/ringNorm/Pconst a_27 <=> a = a_27
% Assm [h4s_canonicals_spolynomu_u_distinctu_c0]: !a_27 a. ~(happ h4/canonical/SPvar a = happ h4/canonical/SPconst a_27)
% Assm [h4s_quotes_indexu_u_distinctu_c0]: !a_27 a. ~(happ h4/quote/Left__idx a = happ h4/quote/Right__idx a_27)
% Assm [h4s_canonicals_spolynomu_u_distinctu_c1]: !a1 a0 a. ~(happ h4/canonical/SPvar a = happ (happ h4/canonical/SPplus a0) a1)
% Assm [h4s_canonicals_spolynomu_u_distinctu_c2]: !a1 a0 a. ~(happ h4/canonical/SPvar a = happ (happ h4/canonical/SPmult a0) a1)
% Assm [h4s_quotes_indexu_u_distinctu_c1]: !a. ~(happ h4/quote/Left__idx a = h4/quote/End__idx)
% Assm [h4s_quotes_indexu_u_distinctu_c2]: !a. ~(happ h4/quote/Right__idx a = h4/quote/End__idx)
% Assm [h4s_quotes_indexu_u_Axiom]: !f2 f1 f0. ?fn. (!a. happ fn (happ h4/quote/Left__idx a) = happ (happ f0 a) (happ fn a)) /\ (!a. happ fn (happ h4/quote/Right__idx a) = happ (happ f1 a) (happ fn a)) /\ happ fn h4/quote/End__idx = f2
% Assm [h4s_quotes_indexu_u_11u_c0]: !a_27 a. happ h4/quote/Left__idx a = happ h4/quote/Left__idx a_27 <=> a = a_27
% Assm [h4s_quotes_indexu_u_compareu_u_defu_c5]: !n_27 m_27. h4/quote/index__compare (happ h4/quote/Left__idx n_27) (happ h4/quote/Left__idx m_27) = h4/quote/index__compare n_27 m_27
% Assm [h4s_quotes_hiddenu_u_u_u_20u_u_40indu_u_u_u_typequote1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/quote/_20_40ind__typequote1 x = h4/quote/_20_40ind__typequote3 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS (h4/quote/_20_40ind__typequote4 x) _0)))
% Assm [h4s_quotes_hiddenu_u_u_u_20u_u_40indu_u_u_u_typequote0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/quote/_20_40ind__typequote0 x = h4/quote/_20_40ind__typequote3 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (h4/ind__type/FCONS (h4/quote/_20_40ind__typequote4 x) _0)))
% Assm [h4s_quotes_indexu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27index_27. (!a00. (?a. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (h4/ind__type/FCONS a _0) /\ happ _27index_27 a) \/ (?a. a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a _0) /\ happ _27index_27 a) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB _0 ==> happ _27index_27 a00) ==> happ _27index_27 r) <=> h4/quote/_20_40ind__typequote4 (h4/quote/_20_40ind__typequote3 r) = r)
% Assm [h4s_quotes_indexu_u_repfnsu_c0]: !a. h4/quote/_20_40ind__typequote3 (h4/quote/_20_40ind__typequote4 a) = a
% Assm [h4s_quotes_Leftu_u_idx0]: h4/quote/Left__idx = h4/quote/_20_40ind__typequote0
% Assm [h4s_quotes_hiddenu_u_u_u_20u_u_40indu_u_u_u_typequote2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/quote/_20_40ind__typequote2 = h4/quote/_20_40ind__typequote3 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB _0)
% Assm [h4s_quotes_Rightu_u_idx0]: h4/quote/Right__idx = h4/quote/_20_40ind__typequote1
% Assm [h4s_quotes_Endu_u_idx0]: h4/quote/End__idx = h4/quote/_20_40ind__typequote2
% Assm [h4s_canonicals_SPmult0]: h4/canonical/SPmult = h4/canonical/_20_40ind__typecanonical8
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical8u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/canonical/_20_40ind__typecanonical8 x) x' = h4/canonical/_20_40ind__typecanonical9 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/canonical/_20_40ind__typecanonical10 x) (h4/ind__type/FCONS (h4/canonical/_20_40ind__typecanonical10 x') _0))))
% Assm [h4s_canonicals_SPvar0]: h4/canonical/SPvar = h4/canonical/_20_40ind__typecanonical5
% Assm [h4s_canonicals_SPconst0]: h4/canonical/SPconst = h4/canonical/_20_40ind__typecanonical6
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical6u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/canonical/_20_40ind__typecanonical6 x = h4/canonical/_20_40ind__typecanonical9 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB x) _0))
% Assm [h4s_canonicals_SPplus0]: h4/canonical/SPplus = h4/canonical/_20_40ind__typecanonical7
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical7u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/canonical/_20_40ind__typecanonical7 x) x' = h4/canonical/_20_40ind__typecanonical9 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/canonical/_20_40ind__typecanonical10 x) (h4/ind__type/FCONS (h4/canonical/_20_40ind__typecanonical10 x') _0))))
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical5u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/canonical/_20_40ind__typecanonical5 x = h4/canonical/_20_40ind__typecanonical9 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C x h4/bool/ARB) _0))
% Assm [h4s_canonicals_spolynomu_u_repfnsu_c0]: !a. h4/canonical/_20_40ind__typecanonical9 (h4/canonical/_20_40ind__typecanonical10 a) = a
% Assm [h4s_canonicals_spolynomu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27spolynom_27. (!a0_270. (?a. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a h4/bool/ARB) _0) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a) _0) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27spolynom_27 a0 /\ happ _27spolynom_27 a1) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27spolynom_27 a0 /\ happ _27spolynom_27 a1) ==> happ _27spolynom_27 a0_270) ==> happ _27spolynom_27 r) <=> h4/canonical/_20_40ind__typecanonical10 (h4/canonical/_20_40ind__typecanonical9 r) = r)
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_quotes_indexu_u_compareu_u_curriedu_u_def]: !x1 x. h4/quote/index__compare x x1 = happ h4/quote/index__compare__tupled (h4/pair/_2C x x1)
% Assm [h4s_quotes_indexu_u_compareu_u_tupledu_u_primitiveu_u_def]: !_9. (!m_27_27_27_27. happ _9 m_27_27_27_27 = h4/combin/I h4/prelim/GREATER) ==> (!_8. (!v1 _6 index__compare__tupled n_27_27. happ (happ (happ (happ _8 v1) _6) index__compare__tupled) n_27_27 = h4/quote/index__CASE v1 _9 (happ (happ _6 index__compare__tupled) n_27_27) (h4/combin/I h4/prelim/GREATER)) ==> (!_7. (!m_27_27. happ _7 m_27_27 = h4/combin/I h4/prelim/LESS) ==> (!_6. (!index__compare__tupled n_27 m_27. happ (happ (happ _6 index__compare__tupled) n_27) m_27 = h4/combin/I (happ index__compare__tupled (h4/pair/_2C n_27 m_27))) ==> (!_5. (!v1 index__compare__tupled n_27. happ (happ (happ _5 v1) index__compare__tupled) n_27 = h4/quote/index__CASE v1 (happ (happ _6 index__compare__tupled) n_27) _7 (h4/combin/I h4/prelim/GREATER)) ==> (!_4. (!v index__compare__tupled v1. happ (happ (happ _4 v) index__compare__tupled) v1 = h4/quote/index__CASE v (happ (happ _5 v1) index__compare__tupled) (happ (happ (happ _8 v1) _6) index__compare__tupled) (h4/quote/index__CASE v1 _7 _7 (h4/combin/I h4/prelim/EQUAL))) ==> (!_3. (!index__compare__tupled v. happ (happ _3 index__compare__tupled) v = happ (happ _4 v) index__compare__tupled) ==> (!_2. (!index__compare__tupled a. happ (happ _2 index__compare__tupled) a = h4/pair/pair__CASE a (happ _3 index__compare__tupled)) ==> (!_1. (!index__compare__tupled. happ _1 index__compare__tupled = happ _2 index__compare__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!m_27 n_27. happ (happ R (h4/pair/_2C n_27 m_27)) (h4/pair/_2C (happ h4/quote/Left__idx n_27) (happ h4/quote/Left__idx m_27))) /\ (!m_27 n_27. happ (happ R (h4/pair/_2C n_27 m_27)) (h4/pair/_2C (happ h4/quote/Right__idx n_27) (happ h4/quote/Right__idx m_27)))) ==> h4/quote/index__compare__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))
% Assm [h4s_quotes_indexu_u_sizeu_u_defu_c1]: !a. h4/quote/index__size (happ h4/quote/Right__idx a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/quote/index__size a)
% Assm [h4s_quotes_indexu_u_sizeu_u_defu_c0]: !a. h4/quote/index__size (happ h4/quote/Left__idx a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/quote/index__size a)
% Assm [h4s_quotes_indexu_u_caseu_u_defu_c1]: !v f1 f a. h4/quote/index__CASE (happ h4/quote/Right__idx a) f f1 v = happ f1 a
% Assm [h4s_quotes_indexu_u_caseu_u_defu_c2]: !v f1 f. h4/quote/index__CASE h4/quote/End__idx f f1 v = v
% Assm [h4s_quotes_indexu_u_caseu_u_defu_c0]: !v f1 f a. h4/quote/index__CASE (happ h4/quote/Left__idx a) f f1 v = happ f a
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_numerals_numeralu_u_distribu_c21]: !n. happ (happ h4/prim__rec/_3C h4/num/0) (h4/arithmetic/NUMERAL n) <=> happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) n
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% 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_INVu_u_IMP]: !A. A ==> ~A ==> F
% Goal: !a1 a0 a. ~(happ h4/ringNorm/Pvar a = happ (happ h4/ringNorm/Pplus a0) a1)
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_Q1383847,TV_Q1383843]: ![V_f, V_g]: (![V_x]: s(TV_Q1383843,happ(s(t_fun(TV_Q1383847,TV_Q1383843),V_f),s(TV_Q1383847,V_x))) = s(TV_Q1383843,happ(s(t_fun(TV_Q1383847,TV_Q1383843),V_g),s(TV_Q1383847,V_x))) => s(t_fun(TV_Q1383847,TV_Q1383843),V_f) = s(t_fun(TV_Q1383847,TV_Q1383843),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_ringNorms_polynomu_u_11u_c2, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pplus),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1))) = s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pplus),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0u_27))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1u_27))) <=> (s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0) = s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0u_27) & s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1) = s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1u_27)))).
fof(ah4s_ringNorms_polynomu_u_sizeu_u_defu_c2, axiom, ![TV_u_27a]: ![V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_ringnorms_polynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pplus),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_ringnorms_polynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_nums_num,h4s_ringnorms_polynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1)))))))).
fof(ah4s_ringNorms_Pplus0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pplus) = s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_u_20u_40indu_u_typeringnorm2)).
fof(ah4s_ringNorms_Pvar0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pvar) = s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm0)).
fof(ah4s_ringNorms_datatypeu_u_polynom, axiom, ![TV_u_27a]: ![V_polynom]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),t_bool),happ(s(t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),t_bool)),happ(s(t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),t_bool)))),happ(s(t_fun(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),t_fun(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),t_bool))))),V_polynom),s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pvar))),s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pconst))),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pplus))),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pmult))),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_popp))))))).
fof(ah4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm4u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm4),s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))) = s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))))).
fof(ah4s_ringNorms_polynomu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_a))))) = s(t_h4s_ringNorms_polynom(TV_u_27a),V_a)).
fof(ah4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm2u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_u_20u_40indu_u_typeringnorm2),s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_xi_))) = s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))))))).
fof(ah4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm3u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_u_20u_40indu_u_typeringnorm3),s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_xi_))) = s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))))))).
fof(ah4s_ringNorms_polynomu_u_distinctu_c0, axiom, ![TV_u_27a]: ![V_au_27, V_a]: ~ (s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pvar),s(t_h4s_quotes_index,V_a))) = s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pconst),s(TV_u_27a,V_au_27))))).
fof(ah4s_ringNorms_polynomu_u_11u_c0, axiom, ![TV_u_27a]: ![V_au_27, V_a]: (s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pvar),s(t_h4s_quotes_index,V_a))) = s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pvar),s(t_h4s_quotes_index,V_au_27))) <=> s(t_h4s_quotes_index,V_a) = s(t_h4s_quotes_index,V_au_27))).
fof(ah4s_ringNorms_polynomu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f4, V_f3, V_f2, V_f1, V_f, V_a]: s(TV_u_27b,h4s_ringnorms_polynomu_u_case(s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pvar),s(t_h4s_quotes_index,V_a))),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f2),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f3),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b),V_f4))) = s(TV_u_27b,happ(s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_h4s_quotes_index,V_a)))).
fof(ah4s_ringNorms_polynomu_u_sizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(t_h4s_nums_num,h4s_ringnorms_polynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pvar),s(t_h4s_quotes_index,V_a))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_h4s_nums_num,h4s_quotes_indexu_u_size(s(t_h4s_quotes_index,V_a)))))).
fof(ah4s_ringNorms_polynomu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27polynomu_27]: (![V_a0u_270]: ((?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_a),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,V_a))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1)))))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1)))))) | ?[V_a]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r)))).
fof(ah4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm0),s(t_h4s_quotes_index,V_x))) = s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_x),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))).
fof(ah4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm1),s(TV_u_27a,V_x))) = s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))).
fof(ah4s_ringNorms_Pmult0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pmult) = s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_u_20u_40indu_u_typeringnorm3)).
fof(ah4s_ringNorms_Pconst0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pconst) = s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm1)).
fof(ah4s_ringNorms_Popp0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_popp) = s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm4)).
fof(ah4s_bools_MONOu_u_EXISTS, 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_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
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_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
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_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => 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,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_bools_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_ringNorms_polynomu_u_TYu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_1),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_uu_0]: (![V_a0u_27]: (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_0),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_27)))) <=> ![V_uu_27polynomu_27]: (![V_a0u_270]: ((?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_a),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_1))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,V_a))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_1))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_1))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1)))))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_1))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1)))))) | ?[V_a]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_1))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_27)))))) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_0),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_rep))))))).
fof(ah4s_bools_ABSu_u_REPu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: (?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ?[V_rep, V_abs]: (![V_a]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a))))) = s(TV_u_27b,V_a) & ![V_r]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_r)))) <=> s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,V_r))))) = s(TV_u_27a,V_r))))).
fof(ah4s_ringNorms_polynomu_u_caseu_u_defu_c2, axiom, ![TV_u_27b,TV_u_27a]: ![V_f4, V_f3, V_f2, V_f1, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_ringnorms_polynomu_u_case(s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pplus),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1))),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f2),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f3),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b),V_f4))) = s(TV_u_27b,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f2),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_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_ringNorms_polynomu_u_11u_c3, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pmult),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1))) = s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pmult),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0u_27))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1u_27))) <=> (s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0) = s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0u_27) & s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1) = s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1u_27)))).
fof(ah4s_ringNorms_polynomu_u_sizeu_u_defu_c3, axiom, ![TV_u_27a]: ![V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_ringnorms_polynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pmult),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_ringnorms_polynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_nums_num,h4s_ringnorms_polynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1)))))))).
fof(ah4s_ringNorms_polynomu_u_sizeu_u_defu_c4, axiom, ![TV_u_27a]: ![V_f, V_a]: s(t_h4s_nums_num,h4s_ringnorms_polynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_popp),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_h4s_nums_num,h4s_ringnorms_polynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a)))))).
fof(ah4s_ringNorms_polynomu_u_11u_c4, axiom, ![TV_u_27a]: ![V_au_27, V_a]: (s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_popp),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a))) = s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_popp),s(t_h4s_ringNorms_polynom(TV_u_27a),V_au_27))) <=> s(t_h4s_ringNorms_polynom(TV_u_27a),V_a) = s(t_h4s_ringNorms_polynom(TV_u_27a),V_au_27))).
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_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> 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_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (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_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
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_ringNorms_polynomu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_f4, V_f3, V_f2, V_f1, V_f, V_a]: s(TV_u_27b,h4s_ringnorms_polynomu_u_case(s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pconst),s(TV_u_27a,V_a))),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f2),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f3),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b),V_f4))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27a,V_a)))).
fof(ah4s_ringNorms_polynomu_u_caseu_u_defu_c4, axiom, ![TV_u_27b,TV_u_27a]: ![V_f4, V_f3, V_f2, V_f1, V_f, V_a]: s(TV_u_27b,h4s_ringnorms_polynomu_u_case(s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_popp),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a))),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f2),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f3),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b),V_f4))) = s(TV_u_27b,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b),V_f4),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a)))).
fof(ah4s_ringNorms_polynomu_u_caseu_u_defu_c3, axiom, ![TV_u_27b,TV_u_27a]: ![V_f4, V_f3, V_f2, V_f1, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_ringnorms_polynomu_u_case(s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pmult),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1))),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f2),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f3),s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b),V_f4))) = s(TV_u_27b,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27b)),V_f3),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1)))).
fof(ah4s_ringNorms_polynomu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a]: s(t_h4s_nums_num,h4s_ringnorms_polynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pconst),s(TV_u_27a,V_a))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a)))))).
fof(ah4s_ringNorms_polynomu_u_11u_c1, axiom, ![TV_u_27a]: ![V_au_27, V_a]: (s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pconst),s(TV_u_27a,V_a))) = s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pconst),s(TV_u_27a,V_au_27))) <=> s(TV_u_27a,V_a) = s(TV_u_27a,V_au_27))).
fof(ah4s_canonicals_spolynomu_u_distinctu_c0, axiom, ![TV_u_27a]: ![V_au_27, V_a]: ~ (s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst),s(TV_u_27a,V_au_27))))).
fof(ah4s_quotes_indexu_u_distinctu_c0, axiom, ![V_au_27, V_a]: ~ (s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_a))) = s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_rightu_u_idx),s(t_h4s_quotes_index,V_au_27))))).
fof(ah4s_canonicals_spolynomu_u_distinctu_c1, axiom, ![TV_u_27a]: ![V_a1, V_a0, V_a]: ~ (s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))))).
fof(ah4s_canonicals_spolynomu_u_distinctu_c2, axiom, ![TV_u_27a]: ![V_a1, V_a0, V_a]: ~ (s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))))).
fof(ah4s_quotes_indexu_u_distinctu_c1, axiom, ![V_a]: ~ (s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_a))) = s(t_h4s_quotes_index,h4s_quotes_endu_u_idx))).
fof(ah4s_quotes_indexu_u_distinctu_c2, axiom, ![V_a]: ~ (s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_rightu_u_idx),s(t_h4s_quotes_index,V_a))) = s(t_h4s_quotes_index,h4s_quotes_endu_u_idx))).
fof(ah4s_quotes_indexu_u_Axiom, axiom, ![TV_u_27a]: ![V_f2, V_f1, V_f0]: ?[V_fn]: (![V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_quotes_index,TV_u_27a),V_fn),s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_a))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_fun(TV_u_27a,TV_u_27a)),V_f0),s(t_h4s_quotes_index,V_a))),s(TV_u_27a,happ(s(t_fun(t_h4s_quotes_index,TV_u_27a),V_fn),s(t_h4s_quotes_index,V_a))))) & (![V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_quotes_index,TV_u_27a),V_fn),s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_rightu_u_idx),s(t_h4s_quotes_index,V_a))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_fun(TV_u_27a,TV_u_27a)),V_f1),s(t_h4s_quotes_index,V_a))),s(TV_u_27a,happ(s(t_fun(t_h4s_quotes_index,TV_u_27a),V_fn),s(t_h4s_quotes_index,V_a))))) & s(TV_u_27a,happ(s(t_fun(t_h4s_quotes_index,TV_u_27a),V_fn),s(t_h4s_quotes_index,h4s_quotes_endu_u_idx))) = s(TV_u_27a,V_f2)))).
fof(ah4s_quotes_indexu_u_11u_c0, axiom, ![V_au_27, V_a]: (s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_a))) = s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_au_27))) <=> s(t_h4s_quotes_index,V_a) = s(t_h4s_quotes_index,V_au_27))).
fof(ah4s_quotes_indexu_u_compareu_u_defu_c5, axiom, ![V_nu_27, V_mu_27]: s(t_h4s_prelims_ordering,h4s_quotes_indexu_u_compare(s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_nu_27))),s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_mu_27))))) = s(t_h4s_prelims_ordering,h4s_quotes_indexu_u_compare(s(t_h4s_quotes_index,V_nu_27),s(t_h4s_quotes_index,V_mu_27)))).
fof(ah4s_quotes_hiddenu_u_u_u_20u_u_40indu_u_u_u_typequote1u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_u_20u_40indu_u_typequote1),s(t_h4s_quotes_index,V_x))) = s(t_h4s_quotes_index,h4s_quotes_u_20u_40indu_u_typequote3(s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),h4s_quotes_u_20u_40indu_u_typequote4(s(t_h4s_quotes_index,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))))))).
fof(ah4s_quotes_hiddenu_u_u_u_20u_u_40indu_u_u_u_typequote0u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_u_20u_40indu_u_typequote0),s(t_h4s_quotes_index,V_x))) = s(t_h4s_quotes_index,h4s_quotes_u_20u_40indu_u_typequote3(s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),h4s_quotes_u_20u_40indu_u_typequote4(s(t_h4s_quotes_index,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))))))).
fof(ah4s_quotes_indexu_u_repfnsu_c1, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27indexu_27]: (![V_a00]: ((?[V_a]: (s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27indexu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a))))) | (?[V_a]: (s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27indexu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a))))) | s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27indexu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27indexu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_bool),h4s_quotes_u_20u_40indu_u_typequote4(s(t_h4s_quotes_index,h4s_quotes_u_20u_40indu_u_typequote3(s(t_h4s_indu_u_types_recspace(t_bool),V_r))))) = s(t_h4s_indu_u_types_recspace(t_bool),V_r)))).
fof(ah4s_quotes_indexu_u_repfnsu_c0, axiom, ![V_a]: s(t_h4s_quotes_index,h4s_quotes_u_20u_40indu_u_typequote3(s(t_h4s_indu_u_types_recspace(t_bool),h4s_quotes_u_20u_40indu_u_typequote4(s(t_h4s_quotes_index,V_a))))) = s(t_h4s_quotes_index,V_a)).
fof(ah4s_quotes_Leftu_u_idx0, axiom, s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx) = s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_u_20u_40indu_u_typequote0)).
fof(ah4s_quotes_hiddenu_u_u_u_20u_u_40indu_u_u_u_typequote2u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => s(t_h4s_quotes_index,h4s_quotes_u_20u_40indu_u_typequote2) = s(t_h4s_quotes_index,h4s_quotes_u_20u_40indu_u_typequote3(s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))))).
fof(ah4s_quotes_Rightu_u_idx0, axiom, s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_rightu_u_idx) = s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_u_20u_40indu_u_typequote1)).
fof(ah4s_quotes_Endu_u_idx0, axiom, s(t_h4s_quotes_index,h4s_quotes_endu_u_idx) = s(t_h4s_quotes_index,h4s_quotes_u_20u_40indu_u_typequote2)).
fof(ah4s_canonicals_SPmult0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult) = s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_u_20u_40indu_u_typecanonical8)).
fof(ah4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical8u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_u_20u_40indu_u_typecanonical8),s(t_h4s_canonicals_spolynom(TV_u_27a),V_x))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_xi_))) = s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))))))).
fof(ah4s_canonicals_SPvar0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar) = s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical5)).
fof(ah4s_canonicals_SPconst0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst) = s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical6)).
fof(ah4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical6u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical6),s(TV_u_27a,V_x))) = s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))).
fof(ah4s_canonicals_SPplus0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus) = s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_u_20u_40indu_u_typecanonical7)).
fof(ah4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical7u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_u_20u_40indu_u_typecanonical7),s(t_h4s_canonicals_spolynom(TV_u_27a),V_x))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_xi_))) = s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))))))).
fof(ah4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical5u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical5),s(t_h4s_quotes_index,V_x))) = s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_x),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))).
fof(ah4s_canonicals_spolynomu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),V_a))))) = s(t_h4s_canonicals_spolynom(TV_u_27a),V_a)).
fof(ah4s_canonicals_spolynomu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27spolynomu_27]: (![V_a0u_270]: ((?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_a),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,V_a))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1)))))) | ?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r)))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (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,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
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_quotes_indexu_u_compareu_u_curriedu_u_def, axiom, ![V_x1, V_x]: s(t_h4s_prelims_ordering,h4s_quotes_indexu_u_compare(s(t_h4s_quotes_index,V_x),s(t_h4s_quotes_index,V_x1))) = s(t_h4s_prelims_ordering,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),h4s_quotes_indexu_u_compareu_u_tupled),s(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_x),s(t_h4s_quotes_index,V_x1)))))).
fof(ah4s_quotes_indexu_u_compareu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_9]: (![V_mu_27u_27u_27u_27]: s(t_h4s_prelims_ordering,happ(s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),V_uu_9),s(t_h4s_quotes_index,V_mu_27u_27u_27u_27))) = s(t_h4s_prelims_ordering,h4s_combins_i(s(t_h4s_prelims_ordering,h4s_prelims_greater))) => ![V_uu_8]: (![V_v1, V_uu_6, V_indexu_u_compareu_u_tupled, V_nu_27u_27]: s(t_h4s_prelims_ordering,happ(s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)))),V_uu_8),s(t_h4s_quotes_index,V_v1))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_6))),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))),s(t_h4s_quotes_index,V_nu_27u_27))) = s(t_h4s_prelims_ordering,h4s_quotes_indexu_u_case(s(t_h4s_quotes_index,V_v1),s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),V_uu_9),s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))),s(t_h4s_quotes_index,V_nu_27u_27))),s(t_h4s_prelims_ordering,h4s_combins_i(s(t_h4s_prelims_ordering,h4s_prelims_greater))))) => ![V_uu_7]: (![V_mu_27u_27]: s(t_h4s_prelims_ordering,happ(s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),V_uu_7),s(t_h4s_quotes_index,V_mu_27u_27))) = s(t_h4s_prelims_ordering,h4s_combins_i(s(t_h4s_prelims_ordering,h4s_prelims_less))) => ![V_uu_6]: (![V_indexu_u_compareu_u_tupled, V_nu_27, V_mu_27]: s(t_h4s_prelims_ordering,happ(s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))),s(t_h4s_quotes_index,V_nu_27))),s(t_h4s_quotes_index,V_mu_27))) = s(t_h4s_prelims_ordering,h4s_combins_i(s(t_h4s_prelims_ordering,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled),s(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_nu_27),s(t_h4s_quotes_index,V_mu_27))))))) => ![V_uu_5]: (![V_v1, V_indexu_u_compareu_u_tupled, V_nu_27]: s(t_h4s_prelims_ordering,happ(s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_5),s(t_h4s_quotes_index,V_v1))),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))),s(t_h4s_quotes_index,V_nu_27))) = s(t_h4s_prelims_ordering,h4s_quotes_indexu_u_case(s(t_h4s_quotes_index,V_v1),s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))),s(t_h4s_quotes_index,V_nu_27))),s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),V_uu_7),s(t_h4s_prelims_ordering,h4s_combins_i(s(t_h4s_prelims_ordering,h4s_prelims_greater))))) => ![V_uu_4]: (![V_v, V_indexu_u_compareu_u_tupled, V_v1]: s(t_h4s_prelims_ordering,happ(s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_4),s(t_h4s_quotes_index,V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))),s(t_h4s_quotes_index,V_v1))) = s(t_h4s_prelims_ordering,h4s_quotes_indexu_u_case(s(t_h4s_quotes_index,V_v),s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_5),s(t_h4s_quotes_index,V_v1))),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))),s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)))),V_uu_8),s(t_h4s_quotes_index,V_v1))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_6))),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))),s(t_h4s_prelims_ordering,h4s_quotes_indexu_u_case(s(t_h4s_quotes_index,V_v1),s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),V_uu_7),s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),V_uu_7),s(t_h4s_prelims_ordering,h4s_combins_i(s(t_h4s_prelims_ordering,h4s_prelims_equal))))))) => ![V_uu_3]: (![V_indexu_u_compareu_u_tupled, V_v]: s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))),s(t_h4s_quotes_index,V_v))) = s(t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_4),s(t_h4s_quotes_index,V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))) => ![V_uu_2]: (![V_indexu_u_compareu_u_tupled, V_a]: s(t_h4s_prelims_ordering,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),V_a))) = s(t_h4s_prelims_ordering,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),V_a),s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))))) => ![V_uu_1]: (![V_indexu_u_compareu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),V_indexu_u_compareu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_bool)),V_R)))) & (![V_mu_27, V_nu_27]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_nu_27),s(t_h4s_quotes_index,V_mu_27))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),h4s_pairs_u_2c(s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_nu_27))),s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_mu_27)))))))) & ![V_mu_27, V_nu_27]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_nu_27),s(t_h4s_quotes_index,V_mu_27))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),h4s_pairs_u_2c(s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_rightu_u_idx),s(t_h4s_quotes_index,V_nu_27))),s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_rightu_u_idx),s(t_h4s_quotes_index,V_mu_27))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),h4s_quotes_indexu_u_compareu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering),t_fun(t_h4s_pairs_prod(t_h4s_quotes_index,t_h4s_quotes_index),t_h4s_prelims_ordering)),V_uu_1)))))))))))))).
fof(ah4s_quotes_indexu_u_sizeu_u_defu_c1, axiom, ![V_a]: s(t_h4s_nums_num,h4s_quotes_indexu_u_size(s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_rightu_u_idx),s(t_h4s_quotes_index,V_a))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_h4s_nums_num,h4s_quotes_indexu_u_size(s(t_h4s_quotes_index,V_a)))))).
fof(ah4s_quotes_indexu_u_sizeu_u_defu_c0, axiom, ![V_a]: s(t_h4s_nums_num,h4s_quotes_indexu_u_size(s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_a))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_h4s_nums_num,h4s_quotes_indexu_u_size(s(t_h4s_quotes_index,V_a)))))).
fof(ah4s_quotes_indexu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_v, V_f1, V_f, V_a]: s(TV_u_27a,h4s_quotes_indexu_u_case(s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_rightu_u_idx),s(t_h4s_quotes_index,V_a))),s(t_fun(t_h4s_quotes_index,TV_u_27a),V_f),s(t_fun(t_h4s_quotes_index,TV_u_27a),V_f1),s(TV_u_27a,V_v))) = s(TV_u_27a,happ(s(t_fun(t_h4s_quotes_index,TV_u_27a),V_f1),s(t_h4s_quotes_index,V_a)))).
fof(ah4s_quotes_indexu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_v, V_f1, V_f]: s(TV_u_27a,h4s_quotes_indexu_u_case(s(t_h4s_quotes_index,h4s_quotes_endu_u_idx),s(t_fun(t_h4s_quotes_index,TV_u_27a),V_f),s(t_fun(t_h4s_quotes_index,TV_u_27a),V_f1),s(TV_u_27a,V_v))) = s(TV_u_27a,V_v)).
fof(ah4s_quotes_indexu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_v, V_f1, V_f, V_a]: s(TV_u_27a,h4s_quotes_indexu_u_case(s(t_h4s_quotes_index,happ(s(t_fun(t_h4s_quotes_index,t_h4s_quotes_index),h4s_quotes_leftu_u_idx),s(t_h4s_quotes_index,V_a))),s(t_fun(t_h4s_quotes_index,TV_u_27a),V_f),s(t_fun(t_h4s_quotes_index,TV_u_27a),V_f1),s(TV_u_27a,V_v))) = s(TV_u_27a,happ(s(t_fun(t_h4s_quotes_index,TV_u_27a),V_f),s(t_h4s_quotes_index,V_a)))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_ltu_c0, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_distribu_c21, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(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_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_xi_)))))).
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_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_bools_DEu_u_MORGANu_u_THMu_c1, 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_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_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
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_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
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_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ch4s_ringNorms_polynomu_u_distinctu_c1, conjecture, ![TV_u_27a]: ![V_a1, V_a0, V_a]: ~ (s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pvar),s(t_h4s_quotes_index,V_a))) = s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pplus),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a0))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_a1))))).
