%   ORIGINAL: h4/binary__ieee/float__nchotomy
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/binary__ieee/float1: h4/binary__ieee/float0 = h4/binary__ieee/_20_40ind__typebinary__ieee0
% Assm: h4/binary__ieee/hidden____20__40ind____typebinary____ieee0____def: h4/binary__ieee/_20_40ind__typebinary__ieee0 = (\a0 a1 a2. h4/binary__ieee/_20_40ind__typebinary__ieee1 ((\a00 a10 a20. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a00 (h4/pair/_2C a10 a20)) (\n. h4/ind__type/BOTTOM)) a0 a1 a2))
% Assm: h4/binary__ieee/float__repfns_c1: !r. (\a0_27. !_27float_27. (!a0_270. (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a00 (h4/pair/_2C a10 a20)) (\n. h4/ind__type/BOTTOM)) a0 a1 a2) ==> _27float_27 a0_270) ==> _27float_27 a0_27) r <=> h4/binary__ieee/_20_40ind__typebinary__ieee2 (h4/binary__ieee/_20_40ind__typebinary__ieee1 r) = r
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/binary__ieee/float__case__cong: !f_27 f M_27 M. M = M_27 /\ (!a0 a1 a2. M_27 = h4/binary__ieee/float0 a0 a1 a2 ==> f a0 a1 a2 = f_27 a0 a1 a2) ==> h4/binary__ieee/float__CASE M f = h4/binary__ieee/float__CASE M_27 f_27
% Assm: h4/binary__ieee/float__Sign0: !c1 c0 c. h4/binary__ieee/float__Sign (h4/binary__ieee/float0 c c0 c1) = c
% Assm: h4/binary__ieee/float__Exponent__fupd0: !f c1 c0 c. h4/binary__ieee/float__Exponent__fupd f (h4/binary__ieee/float0 c c0 c1) = h4/binary__ieee/float0 c (f c0) c1
% Assm: h4/binary__ieee/float__Significand__fupd0: !f c1 c0 c. h4/binary__ieee/float__Significand__fupd f (h4/binary__ieee/float0 c c0 c1) = h4/binary__ieee/float0 c c0 (f c1)
% Assm: h4/binary__ieee/float__Significand0: !c1 c0 c. h4/binary__ieee/float__Significand (h4/binary__ieee/float0 c c0 c1) = c1
% Assm: h4/binary__ieee/float__Sign__fupd0: !f c1 c0 c. h4/binary__ieee/float__Sign__fupd f (h4/binary__ieee/float0 c c0 c1) = h4/binary__ieee/float0 (f c) c0 c1
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% 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/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/binary__ieee/float__repfns_c0: !a. h4/binary__ieee/_20_40ind__typebinary__ieee1 (h4/binary__ieee/_20_40ind__typebinary__ieee2 a) = a
% Assm: h4/binary__ieee/float__Exponent0: !c1 c0 c. h4/binary__ieee/float__Exponent (h4/binary__ieee/float0 c c0 c1) = c0
% Assm: h4/binary__ieee/float__case__def: !f a2 a1 a0. h4/binary__ieee/float__CASE (h4/binary__ieee/float0 a0 a1 a2) f = f a0 a1 a2
% Assm: h4/binary__ieee/float__fn__updates_c0: !f c1 c0 c. h4/binary__ieee/float__Sign__fupd f (h4/binary__ieee/float0 c c0 c1) = h4/binary__ieee/float0 (f c) c0 c1
% Assm: h4/binary__ieee/float__fn__updates_c2: !f c1 c0 c. h4/binary__ieee/float__Significand__fupd f (h4/binary__ieee/float0 c c0 c1) = h4/binary__ieee/float0 c c0 (f c1)
% Assm: h4/binary__ieee/float__fn__updates_c1: !f c1 c0 c. h4/binary__ieee/float__Exponent__fupd f (h4/binary__ieee/float0 c c0 c1) = h4/binary__ieee/float0 c (f c0) c1
% Assm: h4/bool/TRUTH: T
% Assm: h4/binary__ieee/float__accessors_c0: !c1 c0 c. h4/binary__ieee/float__Sign (h4/binary__ieee/float0 c c0 c1) = c
% Assm: h4/binary__ieee/float__accessors_c2: !c1 c0 c. h4/binary__ieee/float__Significand (h4/binary__ieee/float0 c c0 c1) = c1
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/binary__ieee/float__11: !a2_27 a2 a1_27 a1 a0_27 a0. h4/binary__ieee/float0 a0 a1 a2 = h4/binary__ieee/float0 a0_27 a1_27 a2_27 <=> a0 = a0_27 /\ a1 = a1_27 /\ a2 = a2_27
% Assm: h4/binary__ieee/float__size__def: !f1 f a2 a1 a0. h4/binary__ieee/float__size f f1 (h4/binary__ieee/float0 a0 a1 a2) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/binary__ieee/float__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\a0_27. !_27float_27. (!a0_270. (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a00 (h4/pair/_2C a10 a20)) (\n. h4/ind__type/BOTTOM)) a0 a1 a2) ==> _27float_27 a0_270) ==> _27float_27 a0_27) rep
% Assm: h4/binary__ieee/float__accessors_c1: !c1 c0 c. h4/binary__ieee/float__Exponent (h4/binary__ieee/float0 c c0 c1) = c0
% 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/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/binary__ieee/EXISTS__float: !P. (?f. P f) <=> (?c1 c0 c. P (h4/binary__ieee/float__Sign__fupd (h4/combin/K c1) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c0) (h4/binary__ieee/float__Significand__fupd (h4/combin/K c) h4/bool/ARB))))
% Assm: h4/binary__ieee/float__literal__nchotomy: !f. ?c1 c0 c. f = h4/binary__ieee/float__Sign__fupd (h4/combin/K c1) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c0) (h4/binary__ieee/float__Significand__fupd (h4/combin/K c) h4/bool/ARB))
% Assm: h4/binary__ieee/FORALL__float: !P. (!f. P f) <=> (!c1 c0 c. P (h4/binary__ieee/float__Sign__fupd (h4/combin/K c1) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c0) (h4/binary__ieee/float__Significand__fupd (h4/combin/K c) h4/bool/ARB))))
% Assm: h4/binary__ieee/float__literal__11: !c2 c12 c11 c1 c02 c01. h4/binary__ieee/float__Sign__fupd (h4/combin/K c11) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c01) (h4/binary__ieee/float__Significand__fupd (h4/combin/K c1) h4/bool/ARB)) = h4/binary__ieee/float__Sign__fupd (h4/combin/K c12) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c02) (h4/binary__ieee/float__Significand__fupd (h4/combin/K c2) h4/bool/ARB)) <=> c11 = c12 /\ c01 = c02 /\ c1 = c2
% Assm: h4/binary__ieee/float__updates__eq__literal: !f c1 c0 c. h4/binary__ieee/float__Sign__fupd (h4/combin/K c1) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c0) (h4/binary__ieee/float__Significand__fupd (h4/combin/K c) f)) = h4/binary__ieee/float__Sign__fupd (h4/combin/K c1) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c0) (h4/binary__ieee/float__Significand__fupd (h4/combin/K c) h4/bool/ARB))
% Assm: h4/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/binary__ieee/datatype__float: !record float Significand Sign Exponent. h4/bool/DATATYPE (record float Sign Exponent Significand)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/binary__ieee/float__accfupds_c4: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Significand f
% Assm: h4/binary__ieee/float__accfupds_c2: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Exponent f
% Assm: h4/binary__ieee/float__accfupds_c6: !f0 f. h4/binary__ieee/float__Sign (h4/binary__ieee/float__Sign__fupd f0 f) = f0 (h4/binary__ieee/float__Sign f)
% Assm: h4/binary__ieee/float__component__equality: !f2 f1. f1 = f2 <=> h4/binary__ieee/float__Sign f1 = h4/binary__ieee/float__Sign f2 /\ h4/binary__ieee/float__Exponent f1 = h4/binary__ieee/float__Exponent f2 /\ h4/binary__ieee/float__Significand f1 = h4/binary__ieee/float__Significand f2
% Assm: h4/binary__ieee/float__accfupds_c7: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Exponent__fupd f0 f) = f0 (h4/binary__ieee/float__Exponent f)
% Assm: h4/binary__ieee/float__accfupds_c5: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Exponent__fupd f0 f) = h4/binary__ieee/float__Significand f
% Assm: h4/binary__ieee/float__accfupds_c8: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Significand__fupd f0 f) = f0 (h4/binary__ieee/float__Significand f)
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/combin/o__ASSOC: !h g f. h4/combin/o f (h4/combin/o g h) = h4/combin/o (h4/combin/o f g) h
% Assm: h4/binary__ieee/float__fupdfupds__comp_c0: !g f0. h4/combin/o (h4/binary__ieee/float__Sign__fupd f0) (h4/binary__ieee/float__Sign__fupd g) = h4/binary__ieee/float__Sign__fupd (h4/combin/o f0 g)
% Assm: h4/binary__ieee/float__fupdcanon__comp_c3: !h g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/combin/o (h4/binary__ieee/float__Sign__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Sign__fupd g) (h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) h)
% Assm: h4/binary__ieee/float__fupdfupds_c0: !g f0 f. h4/binary__ieee/float__Sign__fupd f0 (h4/binary__ieee/float__Sign__fupd g f) = h4/binary__ieee/float__Sign__fupd (h4/combin/o f0 g) f
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/binary__ieee/float__fupdcanon__comp_c2: !g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/binary__ieee/float__Sign__fupd g) = h4/combin/o (h4/binary__ieee/float__Sign__fupd g) (h4/binary__ieee/float__Significand__fupd f0)
% Assm: h4/binary__ieee/float__fupdcanon_c0: !g f0 f. h4/binary__ieee/float__Exponent__fupd f0 (h4/binary__ieee/float__Sign__fupd g f) = h4/binary__ieee/float__Sign__fupd g (h4/binary__ieee/float__Exponent__fupd f0 f)
% Assm: h4/binary__ieee/float__fupdfupds__comp_c1: !h g f0. h4/combin/o (h4/binary__ieee/float__Sign__fupd f0) (h4/combin/o (h4/binary__ieee/float__Sign__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Sign__fupd (h4/combin/o f0 g)) h
% Assm: h4/binary__ieee/float__accfupds_c1: !f0 f. h4/binary__ieee/float__Sign (h4/binary__ieee/float__Significand__fupd f0 f) = h4/binary__ieee/float__Sign f
% Assm: h4/binary__ieee/float__fupdcanon__comp_c0: !g f0. h4/combin/o (h4/binary__ieee/float__Exponent__fupd f0) (h4/binary__ieee/float__Sign__fupd g) = h4/combin/o (h4/binary__ieee/float__Sign__fupd g) (h4/binary__ieee/float__Exponent__fupd f0)
% Assm: h4/binary__ieee/float__fupdcanon__comp_c1: !h g f0. h4/combin/o (h4/binary__ieee/float__Exponent__fupd f0) (h4/combin/o (h4/binary__ieee/float__Sign__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Sign__fupd g) (h4/combin/o (h4/binary__ieee/float__Exponent__fupd f0) h)
% Assm: h4/binary__ieee/float__fupdcanon_c1: !g f0 f. h4/binary__ieee/float__Significand__fupd f0 (h4/binary__ieee/float__Sign__fupd g f) = h4/binary__ieee/float__Sign__fupd g (h4/binary__ieee/float__Significand__fupd f0 f)
% Assm: h4/binary__ieee/float__accfupds_c0: !f0 f. h4/binary__ieee/float__Sign (h4/binary__ieee/float__Exponent__fupd f0 f) = h4/binary__ieee/float__Sign f
% Assm: h4/binary__ieee/float__fupdfupds_c2: !g f0 f. h4/binary__ieee/float__Significand__fupd f0 (h4/binary__ieee/float__Significand__fupd g f) = h4/binary__ieee/float__Significand__fupd (h4/combin/o f0 g) f
% Assm: h4/binary__ieee/float__fupdfupds__comp_c4: !g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/binary__ieee/float__Significand__fupd g) = h4/binary__ieee/float__Significand__fupd (h4/combin/o f0 g)
% Assm: h4/binary__ieee/float__fupdcanon_c2: !g f0 f. h4/binary__ieee/float__Significand__fupd f0 (h4/binary__ieee/float__Exponent__fupd g f) = h4/binary__ieee/float__Exponent__fupd g (h4/binary__ieee/float__Significand__fupd f0 f)
% Assm: h4/binary__ieee/float__fupdfupds__comp_c2: !g f0. h4/combin/o (h4/binary__ieee/float__Exponent__fupd f0) (h4/binary__ieee/float__Exponent__fupd g) = h4/binary__ieee/float__Exponent__fupd (h4/combin/o f0 g)
% Assm: h4/binary__ieee/float__accfupds_c3: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Significand__fupd f0 f) = h4/binary__ieee/float__Exponent f
% Assm: h4/binary__ieee/float__fupdfupds__comp_c3: !h g f0. h4/combin/o (h4/binary__ieee/float__Exponent__fupd f0) (h4/combin/o (h4/binary__ieee/float__Exponent__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Exponent__fupd (h4/combin/o f0 g)) h
% Assm: h4/binary__ieee/float__fupdfupds_c1: !g f0 f. h4/binary__ieee/float__Exponent__fupd f0 (h4/binary__ieee/float__Exponent__fupd g f) = h4/binary__ieee/float__Exponent__fupd (h4/combin/o f0 g) f
% Assm: h4/binary__ieee/float__fupdcanon__comp_c5: !h g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/combin/o (h4/binary__ieee/float__Exponent__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Exponent__fupd g) (h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) h)
% Assm: h4/binary__ieee/float__fupdcanon__comp_c4: !g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/binary__ieee/float__Exponent__fupd g) = h4/combin/o (h4/binary__ieee/float__Exponent__fupd g) (h4/binary__ieee/float__Significand__fupd f0)
% Assm: h4/binary__ieee/float__fupdfupds__comp_c5: !h g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/combin/o (h4/binary__ieee/float__Significand__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Significand__fupd (h4/combin/o f0 g)) h
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/words/word__join__def: !w v. h4/words/word__join v w = h4/bool/LET (h4/bool/LET (\cv cw. h4/words/word__or (h4/words/word__lsl cv (h4/fcp/dimindex h4/bool/the__value)) cw) (h4/words/w2w v)) (h4/words/w2w w)
% Assm: h4/words/word__join__index: !i b a. h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> (h4/fcp/fcp__index (h4/words/word__join a b) i <=> h4/bool/COND (h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value)) (h4/fcp/fcp__index b i) (h4/fcp/fcp__index a (h4/arithmetic/_2D i (h4/fcp/dimindex h4/bool/the__value))))
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/words/w2w0: !w i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> (h4/fcp/fcp__index (h4/words/w2w w) i <=> h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) /\ h4/fcp/fcp__index w i)
% Assm: h4/words/DIMINDEX__GT__0: h4/prim__rec/_3C h4/num/0 (h4/fcp/dimindex h4/bool/the__value)
% Assm: h4/fcp/index__sum: h4/fcp/dimindex h4/bool/the__value = h4/bool/COND (h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/pred__set/FINITE h4/pred__set/UNIV) (h4/arithmetic/_2B (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/words/word__or__def: !w v. h4/words/word__or v w = h4/fcp/FCP (\i. h4/fcp/fcp__index v i \/ h4/fcp/fcp__index w i)
% Assm: h4/fcp/FCP__BETA: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index (h4/fcp/FCP g) i = g i
% Assm: h4/words/word__lsl__def: !w n. h4/words/word__lsl w n = h4/fcp/FCP (\i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) /\ h4/arithmetic/_3C_3D n i /\ h4/fcp/fcp__index w (h4/arithmetic/_2D i n))
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% 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/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/arithmetic/SUB__RIGHT__LESS: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2D m n) p <=> h4/prim__rec/_3C m (h4/arithmetic/_2B n p) /\ h4/prim__rec/_3C h4/num/0 p
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% 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/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/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/numeral/numeral__add_c1: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm: h4/arithmetic/NOT__LEQ: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/RIGHT__ADD__DISTRIB: !p n m. h4/arithmetic/_2A (h4/arithmetic/_2B m n) p = h4/arithmetic/_2B (h4/arithmetic/_2A m p) (h4/arithmetic/_2A n p)
% Assm: h4/arithmetic/MULT__LEFT__1: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Goal: !ff. ?c c0 c1. ff = h4/binary__ieee/float0 c c0 c1
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_binaryu_u_ieees_float1]: h4/binary__ieee/float0 = h4/binary__ieee/_20_40ind__typebinary__ieee0
% Assm [h4s_binaryu_u_ieees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typebinaryu_u_u_u_ieee0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x x. happ (happ (happ h4/binary__ieee/_20_40ind__typebinary__ieee0 x) x) x = h4/binary__ieee/_20_40ind__typebinary__ieee1 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C x (h4/pair/_2C x x)) _0))
% Assm [h4s_binaryu_u_ieees_floatu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27float_27. (!a0_270. (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 (h4/pair/_2C a1 a2)) _0) ==> happ _27float_27 a0_270) ==> happ _27float_27 r) <=> h4/binary__ieee/_20_40ind__typebinary__ieee2 (h4/binary__ieee/_20_40ind__typebinary__ieee1 r) = r)
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_binaryu_u_ieees_floatu_u_caseu_u_cong]: !f_27 f M_27 M. M = M_27 /\ (!a0 a1 a2. M_27 = happ (happ (happ h4/binary__ieee/float0 a0) a1) a2 ==> happ (happ (happ f a0) a1) a2 = happ (happ (happ f_27 a0) a1) a2) ==> h4/binary__ieee/float__CASE M f = h4/binary__ieee/float__CASE M_27 f_27
% Assm [h4s_binaryu_u_ieees_floatu_u_Sign0]: !c1 c0 c. h4/binary__ieee/float__Sign (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = c
% Assm [h4s_binaryu_u_ieees_floatu_u_Exponentu_u_fupd0]: !f c1 c0 c. happ (h4/binary__ieee/float__Exponent__fupd f) (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = happ (happ (happ h4/binary__ieee/float0 c) (happ f c0)) c1
% Assm [h4s_binaryu_u_ieees_floatu_u_Significandu_u_fupd0]: !f c1 c0 c. happ (h4/binary__ieee/float__Significand__fupd f) (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = happ (happ (happ h4/binary__ieee/float0 c) c0) (happ f c1)
% Assm [h4s_binaryu_u_ieees_floatu_u_Significand0]: !c1 c0 c. h4/binary__ieee/float__Significand (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = c1
% Assm [h4s_binaryu_u_ieees_floatu_u_Signu_u_fupd0]: !f c1 c0 c. happ (h4/binary__ieee/float__Sign__fupd f) (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = happ (happ (happ h4/binary__ieee/float0 (happ f c)) c0) c1
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% 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_indu_u_types_FCONS0u_c0]: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_binaryu_u_ieees_floatu_u_repfnsu_c0]: !a. h4/binary__ieee/_20_40ind__typebinary__ieee1 (h4/binary__ieee/_20_40ind__typebinary__ieee2 a) = a
% Assm [h4s_binaryu_u_ieees_floatu_u_Exponent0]: !c1 c0 c. h4/binary__ieee/float__Exponent (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = c0
% Assm [h4s_binaryu_u_ieees_floatu_u_caseu_u_def]: !f a2 a1 a0. h4/binary__ieee/float__CASE (happ (happ (happ h4/binary__ieee/float0 a0) a1) a2) f = happ (happ (happ f a0) a1) a2
% Assm [h4s_binaryu_u_ieees_floatu_u_fnu_u_updatesu_c0]: !f c1 c0 c. happ (h4/binary__ieee/float__Sign__fupd f) (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = happ (happ (happ h4/binary__ieee/float0 (happ f c)) c0) c1
% Assm [h4s_binaryu_u_ieees_floatu_u_fnu_u_updatesu_c2]: !f c1 c0 c. happ (h4/binary__ieee/float__Significand__fupd f) (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = happ (happ (happ h4/binary__ieee/float0 c) c0) (happ f c1)
% Assm [h4s_binaryu_u_ieees_floatu_u_fnu_u_updatesu_c1]: !f c1 c0 c. happ (h4/binary__ieee/float__Exponent__fupd f) (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = happ (happ (happ h4/binary__ieee/float0 c) (happ f c0)) c1
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_binaryu_u_ieees_floatu_u_accessorsu_c0]: !c1 c0 c. h4/binary__ieee/float__Sign (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = c
% Assm [h4s_binaryu_u_ieees_floatu_u_accessorsu_c2]: !c1 c0 c. h4/binary__ieee/float__Significand (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = c1
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_binaryu_u_ieees_floatu_u_11]: !a2_27 a2 a1_27 a1 a0_27 a0. happ (happ (happ h4/binary__ieee/float0 a0) a1) a2 = happ (happ (happ h4/binary__ieee/float0 a0_27) a1_27) a2_27 <=> a0 = a0_27 /\ a1 = a1_27 /\ a2 = a2_27
% Assm [h4s_binaryu_u_ieees_floatu_u_sizeu_u_def]: !f1 f a2 a1 a0. h4/binary__ieee/float__size f f1 (happ (happ (happ h4/binary__ieee/float0 a0) a1) a2) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_binaryu_u_ieees_floatu_u_TYu_u_DEF]: !_1. (!n. happ _1 n = h4/ind__type/BOTTOM) ==> (!_0. (!a0_27. happ _0 a0_27 <=> (!_27float_27. (!a0_270. (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 (h4/pair/_2C a1 a2)) _1) ==> happ _27float_27 a0_270) ==> happ _27float_27 a0_27)) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep))
% Assm [h4s_binaryu_u_ieees_floatu_u_accessorsu_c1]: !c1 c0 c. h4/binary__ieee/float__Exponent (happ (happ (happ h4/binary__ieee/float0 c) c0) c1) = c0
% 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_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_binaryu_u_ieees_EXISTSu_u_float]: !P. (?f. happ P f) <=> (?c1 c0 c. happ P (happ (h4/binary__ieee/float__Sign__fupd (h4/combin/K c1)) (happ (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c0)) (happ (h4/binary__ieee/float__Significand__fupd (h4/combin/K c)) h4/bool/ARB))))
% Assm [h4s_binaryu_u_ieees_floatu_u_literalu_u_nchotomy]: !f. ?c1 c0 c. f = happ (h4/binary__ieee/float__Sign__fupd (h4/combin/K c1)) (happ (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c0)) (happ (h4/binary__ieee/float__Significand__fupd (h4/combin/K c)) h4/bool/ARB))
% Assm [h4s_binaryu_u_ieees_FORALLu_u_float]: !P. (!f. happ P f) <=> (!c1 c0 c. happ P (happ (h4/binary__ieee/float__Sign__fupd (h4/combin/K c1)) (happ (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c0)) (happ (h4/binary__ieee/float__Significand__fupd (h4/combin/K c)) h4/bool/ARB))))
% Assm [h4s_binaryu_u_ieees_floatu_u_literalu_u_11]: !c2 c12 c11 c1 c02 c01. happ (h4/binary__ieee/float__Sign__fupd (h4/combin/K c11)) (happ (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c01)) (happ (h4/binary__ieee/float__Significand__fupd (h4/combin/K c1)) h4/bool/ARB)) = happ (h4/binary__ieee/float__Sign__fupd (h4/combin/K c12)) (happ (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c02)) (happ (h4/binary__ieee/float__Significand__fupd (h4/combin/K c2)) h4/bool/ARB)) <=> c11 = c12 /\ c01 = c02 /\ c1 = c2
% Assm [h4s_binaryu_u_ieees_floatu_u_updatesu_u_equ_u_literal]: !f c1 c0 c. happ (h4/binary__ieee/float__Sign__fupd (h4/combin/K c1)) (happ (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c0)) (happ (h4/binary__ieee/float__Significand__fupd (h4/combin/K c)) f)) = happ (h4/binary__ieee/float__Sign__fupd (h4/combin/K c1)) (happ (h4/binary__ieee/float__Exponent__fupd (h4/combin/K c0)) (happ (h4/binary__ieee/float__Significand__fupd (h4/combin/K c)) h4/bool/ARB))
% Assm [h4s_combins_Ku_u_THM]: !y x. happ (h4/combin/K x) y = x
% Assm [h4s_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_binaryu_u_ieees_datatypeu_u_float]: !record float Significand Sign Exponent. h4/bool/DATATYPE (happ (happ (happ (happ record float) Sign) Exponent) Significand)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c4]: !f0 f. h4/binary__ieee/float__Significand (happ (h4/binary__ieee/float__Sign__fupd f0) f) = h4/binary__ieee/float__Significand f
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c2]: !f0 f. h4/binary__ieee/float__Exponent (happ (h4/binary__ieee/float__Sign__fupd f0) f) = h4/binary__ieee/float__Exponent f
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c6]: !f0 f. h4/binary__ieee/float__Sign (happ (h4/binary__ieee/float__Sign__fupd f0) f) = happ f0 (h4/binary__ieee/float__Sign f)
% Assm [h4s_binaryu_u_ieees_floatu_u_componentu_u_equality]: !f2 f1. f1 = f2 <=> h4/binary__ieee/float__Sign f1 = h4/binary__ieee/float__Sign f2 /\ h4/binary__ieee/float__Exponent f1 = h4/binary__ieee/float__Exponent f2 /\ h4/binary__ieee/float__Significand f1 = h4/binary__ieee/float__Significand f2
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c7]: !f0 f. h4/binary__ieee/float__Exponent (happ (h4/binary__ieee/float__Exponent__fupd f0) f) = happ f0 (h4/binary__ieee/float__Exponent f)
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c5]: !f0 f. h4/binary__ieee/float__Significand (happ (h4/binary__ieee/float__Exponent__fupd f0) f) = h4/binary__ieee/float__Significand f
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c8]: !f0 f. h4/binary__ieee/float__Significand (happ (h4/binary__ieee/float__Significand__fupd f0) f) = happ f0 (h4/binary__ieee/float__Significand f)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_combins_ou_u_ASSOC]: !h g f. h4/combin/o f (h4/combin/o g h) = h4/combin/o (h4/combin/o f g) h
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c0]: !g f0. h4/combin/o (h4/binary__ieee/float__Sign__fupd f0) (h4/binary__ieee/float__Sign__fupd g) = h4/binary__ieee/float__Sign__fupd (h4/combin/o f0 g)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c3]: !h g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/combin/o (h4/binary__ieee/float__Sign__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Sign__fupd g) (h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) h)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_c0]: !g f0 f. happ (h4/binary__ieee/float__Sign__fupd f0) (happ (h4/binary__ieee/float__Sign__fupd g) f) = happ (h4/binary__ieee/float__Sign__fupd (h4/combin/o f0 g)) f
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c2]: !g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/binary__ieee/float__Sign__fupd g) = h4/combin/o (h4/binary__ieee/float__Sign__fupd g) (h4/binary__ieee/float__Significand__fupd f0)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdcanonu_c0]: !g f0 f. happ (h4/binary__ieee/float__Exponent__fupd f0) (happ (h4/binary__ieee/float__Sign__fupd g) f) = happ (h4/binary__ieee/float__Sign__fupd g) (happ (h4/binary__ieee/float__Exponent__fupd f0) f)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c1]: !h g f0. h4/combin/o (h4/binary__ieee/float__Sign__fupd f0) (h4/combin/o (h4/binary__ieee/float__Sign__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Sign__fupd (h4/combin/o f0 g)) h
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c1]: !f0 f. h4/binary__ieee/float__Sign (happ (h4/binary__ieee/float__Significand__fupd f0) f) = h4/binary__ieee/float__Sign f
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c0]: !g f0. h4/combin/o (h4/binary__ieee/float__Exponent__fupd f0) (h4/binary__ieee/float__Sign__fupd g) = h4/combin/o (h4/binary__ieee/float__Sign__fupd g) (h4/binary__ieee/float__Exponent__fupd f0)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c1]: !h g f0. h4/combin/o (h4/binary__ieee/float__Exponent__fupd f0) (h4/combin/o (h4/binary__ieee/float__Sign__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Sign__fupd g) (h4/combin/o (h4/binary__ieee/float__Exponent__fupd f0) h)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdcanonu_c1]: !g f0 f. happ (h4/binary__ieee/float__Significand__fupd f0) (happ (h4/binary__ieee/float__Sign__fupd g) f) = happ (h4/binary__ieee/float__Sign__fupd g) (happ (h4/binary__ieee/float__Significand__fupd f0) f)
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c0]: !f0 f. h4/binary__ieee/float__Sign (happ (h4/binary__ieee/float__Exponent__fupd f0) f) = h4/binary__ieee/float__Sign f
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_c2]: !g f0 f. happ (h4/binary__ieee/float__Significand__fupd f0) (happ (h4/binary__ieee/float__Significand__fupd g) f) = happ (h4/binary__ieee/float__Significand__fupd (h4/combin/o f0 g)) f
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c4]: !g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/binary__ieee/float__Significand__fupd g) = h4/binary__ieee/float__Significand__fupd (h4/combin/o f0 g)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdcanonu_c2]: !g f0 f. happ (h4/binary__ieee/float__Significand__fupd f0) (happ (h4/binary__ieee/float__Exponent__fupd g) f) = happ (h4/binary__ieee/float__Exponent__fupd g) (happ (h4/binary__ieee/float__Significand__fupd f0) f)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c2]: !g f0. h4/combin/o (h4/binary__ieee/float__Exponent__fupd f0) (h4/binary__ieee/float__Exponent__fupd g) = h4/binary__ieee/float__Exponent__fupd (h4/combin/o f0 g)
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c3]: !f0 f. h4/binary__ieee/float__Exponent (happ (h4/binary__ieee/float__Significand__fupd f0) f) = h4/binary__ieee/float__Exponent f
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c3]: !h g f0. h4/combin/o (h4/binary__ieee/float__Exponent__fupd f0) (h4/combin/o (h4/binary__ieee/float__Exponent__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Exponent__fupd (h4/combin/o f0 g)) h
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_c1]: !g f0 f. happ (h4/binary__ieee/float__Exponent__fupd f0) (happ (h4/binary__ieee/float__Exponent__fupd g) f) = happ (h4/binary__ieee/float__Exponent__fupd (h4/combin/o f0 g)) f
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c5]: !h g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/combin/o (h4/binary__ieee/float__Exponent__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Exponent__fupd g) (h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) h)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c4]: !g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/binary__ieee/float__Exponent__fupd g) = h4/combin/o (h4/binary__ieee/float__Exponent__fupd g) (h4/binary__ieee/float__Significand__fupd f0)
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c5]: !h g f0. h4/combin/o (h4/binary__ieee/float__Significand__fupd f0) (h4/combin/o (h4/binary__ieee/float__Significand__fupd g) h) = h4/combin/o (h4/binary__ieee/float__Significand__fupd (h4/combin/o f0 g)) h
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_wordss_wordu_u_joinu_u_def]: !_1. (!cv cw. happ (happ _1 cv) cw = h4/words/word__or (h4/words/word__lsl cv (h4/fcp/dimindex h4/bool/the__value)) cw) ==> (!_0. (!cv. happ _0 cv = happ _1 cv) ==> (!w v. h4/words/word__join v w = h4/bool/LET (h4/bool/LET _0 (h4/words/w2w v)) (h4/words/w2w w)))
% Assm [h4s_wordss_wordu_u_joinu_u_index]: !i b a. h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> (h4/fcp/fcp__index (h4/words/word__join a b) i <=> h4/bool/COND (h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value)) (h4/fcp/fcp__index b i) (h4/fcp/fcp__index a (h4/arithmetic/_2D i (h4/fcp/dimindex h4/bool/the__value))))
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_wordss_w2w0]: !w i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> (h4/fcp/fcp__index (h4/words/w2w w) i <=> h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) /\ h4/fcp/fcp__index w i)
% Assm [h4s_wordss_DIMINDEXu_u_GTu_u_0]: h4/prim__rec/_3C h4/num/0 (h4/fcp/dimindex h4/bool/the__value)
% Assm [h4s_fcps_indexu_u_sum]: ?v. (v <=> h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/pred__set/FINITE h4/pred__set/UNIV) /\ h4/fcp/dimindex h4/bool/the__value = h4/bool/COND v (h4/arithmetic/_2B (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_wordss_wordu_u_oru_u_def]: !_0. (!v w i. happ (happ (happ _0 v) w) i <=> h4/fcp/fcp__index v i \/ h4/fcp/fcp__index w i) ==> (!w v. h4/words/word__or v w = h4/fcp/FCP (happ (happ _0 v) w))
% Assm [h4s_fcps_FCPu_u_BETA]: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index (h4/fcp/FCP g) i = happ g i
% Assm [h4s_wordss_wordu_u_lslu_u_def]: !_0. (!w n i. happ (happ (happ _0 w) n) i <=> h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) /\ h4/arithmetic/_3C_3D n i /\ h4/fcp/fcp__index w (h4/arithmetic/_2D i n)) ==> (!w n. h4/words/word__lsl w n = h4/fcp/FCP (happ (happ _0 w) n))
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% 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_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_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_LESS]: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2D m n) p <=> h4/prim__rec/_3C m (h4/arithmetic/_2B n p) /\ h4/prim__rec/_3C h4/num/0 p
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% 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_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_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_numerals_numeralu_u_addu_c1]: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm [h4s_arithmetics_NOTu_u_LEQ]: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_RIGHTu_u_ADDu_u_DISTRIB]: !p n m. h4/arithmetic/_2A (h4/arithmetic/_2B m n) p = h4/arithmetic/_2B (h4/arithmetic/_2A m p) (h4/arithmetic/_2A n p)
% Assm [h4s_arithmetics_MULTu_u_LEFTu_u_1]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Goal: !ff. ?c c0 c1. ff = happ (happ (happ h4/binary__ieee/float0 c) c0) c1
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_Q1179903,TV_Q1179899]: ![V_f, V_g]: (![V_x]: s(TV_Q1179899,happ(s(t_fun(TV_Q1179903,TV_Q1179899),V_f),s(TV_Q1179903,V_x))) = s(TV_Q1179899,happ(s(t_fun(TV_Q1179903,TV_Q1179899),V_g),s(TV_Q1179903,V_x))) => s(t_fun(TV_Q1179903,TV_Q1179899),V_f) = s(t_fun(TV_Q1179903,TV_Q1179899),V_g))).
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_binaryu_u_ieees_float1, axiom, ![TV_u_27t,TV_u_27w]: s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0) = s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee0)).
fof(ah4s_binaryu_u_ieees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typebinaryu_u_u_u_ieee0u_u_u_u_def, axiom, ![TV_u_27w,TV_u_27t]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t))))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),h4s_indu_u_types_bottom) => ![V_x, V_x0, V_x1]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_x))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_x0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_x1))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee1(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t))),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_x),s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_x0),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_x1))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t))))),V_uu_0))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_repfnsu_c1, axiom, ![TV_u_27w,TV_u_27t]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t))))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27floatu_27]: (![V_a0u_270]: (?[V_a0, V_a1, V_a2]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t))),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0),s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t))))),V_uu_0))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),t_bool),V_uu_27floatu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),t_bool),V_uu_27floatu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee2(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee1(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),V_r)))).
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_binaryu_u_ieees_floatu_u_caseu_u_cong, axiom, ![TV_u_27w,TV_u_27t,TV_u_27a]: ![V_fu_27, V_f, V_Mu_27, V_M]: ((s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_M) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_Mu_27) & ![V_a0, V_a1, V_a2]: (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_Mu_27) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2))) => s(TV_u_27a,happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a))),V_f),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2))) = s(TV_u_27a,happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a))),V_fu_27),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2))))) => s(TV_u_27a,h4s_binaryu_u_ieees_floatu_u_case(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_M),s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a))),V_f))) = s(TV_u_27a,h4s_binaryu_u_ieees_floatu_u_case(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_Mu_27),s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a))),V_fu_27))))).
fof(ah4s_binaryu_u_ieees_floatu_u_Sign0, axiom, ![TV_u_27w,TV_u_27t]: ![V_c1, V_c0, V_c]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c)).
fof(ah4s_binaryu_u_ieees_floatu_u_Exponentu_u_fupd0, axiom, ![TV_u_27w,TV_u_27t]: ![V_f, V_c1, V_c0, V_c]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1)))).
fof(ah4s_binaryu_u_ieees_floatu_u_Significandu_u_fupd0, axiom, ![TV_u_27w,TV_u_27t]: ![V_f, V_c1, V_c0, V_c]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_Significand0, axiom, ![TV_u_27w,TV_u_27t]: ![V_c1, V_c0, V_c]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1)).
fof(ah4s_binaryu_u_ieees_floatu_u_Signu_u_fupd0, axiom, ![TV_u_27w,TV_u_27t]: ![V_f, V_c1, V_c0, V_c]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1)))).
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_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_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(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_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_binaryu_u_ieees_floatu_u_repfnsu_c0, axiom, ![TV_u_27t,TV_u_27w]: ![V_a]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee1(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee2(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_a))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_a)).
fof(ah4s_binaryu_u_ieees_floatu_u_Exponent0, axiom, ![TV_u_27t,TV_u_27w]: ![V_c1, V_c0, V_c]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0)).
fof(ah4s_binaryu_u_ieees_floatu_u_caseu_u_def, axiom, ![TV_u_27a,TV_u_27w,TV_u_27t]: ![V_f, V_a2, V_a1, V_a0]: s(TV_u_27a,h4s_binaryu_u_ieees_floatu_u_case(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2))),s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a))),V_f))) = s(TV_u_27a,happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),TV_u_27a))),V_f),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2)))).
fof(ah4s_binaryu_u_ieees_floatu_u_fnu_u_updatesu_c0, axiom, ![TV_u_27w,TV_u_27t]: ![V_f, V_c1, V_c0, V_c]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1)))).
fof(ah4s_binaryu_u_ieees_floatu_u_fnu_u_updatesu_c2, axiom, ![TV_u_27w,TV_u_27t]: ![V_f, V_c1, V_c0, V_c]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fnu_u_updatesu_c1, axiom, ![TV_u_27w,TV_u_27t]: ![V_f, V_c1, V_c0, V_c]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_binaryu_u_ieees_floatu_u_accessorsu_c0, axiom, ![TV_u_27w,TV_u_27t]: ![V_c1, V_c0, V_c]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c)).
fof(ah4s_binaryu_u_ieees_floatu_u_accessorsu_c2, axiom, ![TV_u_27w,TV_u_27t]: ![V_c1, V_c0, V_c]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1)).
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_binaryu_u_ieees_floatu_u_11, axiom, ![TV_u_27w,TV_u_27t]: ![V_a2u_27, V_a2, V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0u_27))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1u_27))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2u_27))) <=> (s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0u_27) & (s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1u_27) & s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2u_27))))).
fof(ah4s_binaryu_u_ieees_floatu_u_sizeu_u_def, axiom, ![TV_u_27w,TV_u_27t]: ![V_f1, V_f, V_a2, V_a1, V_a0]: s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_size(s(t_fun(TV_u_27t,t_h4s_nums_num),V_f),s(t_fun(TV_u_27w,t_h4s_nums_num),V_f1),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_TYu_u_DEF, axiom, ![TV_u_27w,TV_u_27t]: ![V_uu_1]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t))))),V_uu_1),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),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_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),t_bool),V_uu_0),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),V_a0u_27)))) <=> ![V_uu_27floatu_27]: (![V_a0u_270]: (?[V_a0, V_a1, V_a2]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t))),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_a0),s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_a1),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_a2))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t))))),V_uu_1))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),t_bool),V_uu_27floatu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),t_bool),V_uu_27floatu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),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_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t)))),t_bool),V_uu_0),s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27t))))),V_rep))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_accessorsu_c1, axiom, ![TV_u_27t,TV_u_27w]: ![V_c1, V_c0, V_c]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0)).
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_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_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_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_binaryu_u_ieees_EXISTSu_u_float, axiom, ![TV_u_27t,TV_u_27w]: ![V_P]: (?[V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),V_P),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))) <=> ?[V_c1, V_c0, V_c]: p(s(t_bool,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),V_P),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c1))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_arb)))))))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_literalu_u_nchotomy, axiom, ![TV_u_27t,TV_u_27w]: ![V_f]: ?[V_c1, V_c0, V_c]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c1))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_arb)))))))).
fof(ah4s_binaryu_u_ieees_FORALLu_u_float, axiom, ![TV_u_27t,TV_u_27w]: ![V_P]: (![V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),V_P),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))) <=> ![V_c1, V_c0, V_c]: p(s(t_bool,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),V_P),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c1))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_arb)))))))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_literalu_u_11, axiom, ![TV_u_27w,TV_u_27t]: ![V_c2, V_c12, V_c11, V_c1, V_c02, V_c01]: (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c11))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c01))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_arb))))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c12))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c02))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c2))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_arb))))))) <=> (s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c11) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c12) & (s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c01) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c02) & s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c2))))).
fof(ah4s_binaryu_u_ieees_floatu_u_updatesu_u_equ_u_literal, axiom, ![TV_u_27t,TV_u_27w]: ![V_f, V_c1, V_c0, V_c]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c1))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c1))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_arb)))))))).
fof(ah4s_combins_Ku_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(TV_u_27a,V_x)).
fof(ah4s_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_binaryu_u_ieees_datatypeu_u_float, axiom, ![TV_u_27w,TV_u_27t]: ![V_record, V_float, V_Significand, V_Sign, V_Exponent]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_bool)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_bool))),happ(s(t_fun(t_h4s_mins_ind,t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_bool)))),V_record),s(t_h4s_mins_ind,V_float))),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_Sign))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_Exponent))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_Significand))))))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_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_binaryu_u_ieees_floatu_u_accfupdsu_c4, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c2, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c6, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentu_u_equality, axiom, ![TV_u_27t,TV_u_27w]: ![V_f2, V_f1]: (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f1) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f2) <=> (s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f1))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f2))) & (s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f1))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f2))) & s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f1))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f2))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c7, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0),s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c5, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c8, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0),s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_combins_ou_u_ASSOC, axiom, ![TV_u_27b,TV_u_27a,TV_u_27d,TV_u_27c]: ![V_h, V_g, V_f]: s(t_fun(TV_u_27d,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27d,TV_u_27a),h4s_combins_o(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(t_fun(TV_u_27d,TV_u_27c),V_h))))) = s(t_fun(TV_u_27d,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(t_fun(TV_u_27d,TV_u_27c),V_h)))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c0, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0]: s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0))),s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))))) = s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c3, axiom, ![TV_u_27a,TV_u_27t,TV_u_27w]: ![V_h, V_g, V_f0]: s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h))))) = s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_c0, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0, V_f]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
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_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c2, axiom, ![TV_u_27w,TV_u_27t]: ![V_g, V_f0]: s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))))) = s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdcanonu_c0, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0, V_f]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c1, axiom, ![TV_u_27a,TV_u_27t,TV_u_27w]: ![V_h, V_g, V_f0]: s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h))))) = s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h)))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c1, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c0, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0]: s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))))) = s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c1, axiom, ![TV_u_27a,TV_u_27t,TV_u_27w]: ![V_h, V_g, V_f0]: s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h))))) = s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdcanonu_c1, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0, V_f]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c0, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_c2, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0, V_f]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0),s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_g))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c4, axiom, ![TV_u_27w,TV_u_27t]: ![V_g, V_f0]: s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_g))))) = s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0),s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_g)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdcanonu_c2, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0, V_f]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c2, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0]: s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))))) = s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0),s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c3, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c3, axiom, ![TV_u_27a,TV_u_27t,TV_u_27w]: ![V_h, V_g, V_f0]: s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h))))) = s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0),s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h)))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_c1, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0, V_f]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0),s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c5, axiom, ![TV_u_27a,TV_u_27t,TV_u_27w]: ![V_h, V_g, V_f0]: s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h))))) = s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdcanonu_u_compu_c4, axiom, ![TV_u_27w,TV_u_27t]: ![V_g, V_f0]: s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))))) = s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_g))),s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_u_compu_c5, axiom, ![TV_u_27a,TV_u_27t,TV_u_27w]: ![V_h, V_g, V_f0]: s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_g))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h))))) = s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0),s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_g))))),s(t_fun(TV_u_27a,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),V_h)))).
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_wordss_wordu_u_joinu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_cv, V_cw]: s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)))),V_uu_1),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cv))),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cw))) = s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cv),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))))),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cw))) => ![V_uu_0]: (![V_cv]: s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)))),V_uu_0),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cv))) = s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)))),V_uu_1),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cv))) => ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_wordu_u_join(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_w))) = s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_bools_let(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b))),h4s_bools_let(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)))),V_uu_0),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))))),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_w)))))))).
fof(ah4s_wordss_wordu_u_joinu_u_index, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_b, V_a]: ((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ)))) & (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_univ)))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_bools_theu_u_value)))))))) => s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_wordu_u_join(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_b))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))))),s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_b),s(t_h4s_nums_num,V_i))),s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))))))))))).
fof(ah4s_bools_LETu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,h4s_bools_let(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_x)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_wordss_w2w0, axiom, ![TV_u_27b,TV_u_27a]: ![V_w, V_i]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => (p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) & p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,V_i)))))))).
fof(ah4s_wordss_DIMINDEXu_u_GTu_u_0, axiom, ![TV_u_27a]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_fcps_indexu_u_sum, axiom, ![TV_u_27a,TV_u_27b]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ)))) & p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_univ)))))) & s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))).
fof(ah4s_wordss_wordu_u_oru_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_v, V_w, V_i]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i)))) <=> (p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_nums_num,V_i)))) | p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,V_i)))))) => ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_fcps_FCPu_u_BETA, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_g]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => s(TV_u_27a,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g))),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,V_i))))).
fof(ah4s_wordss_wordu_u_lslu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_n, V_i]: (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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_i)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) & (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_i)))) & p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n))))))))) => ![V_w, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(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_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_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_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_LESS, axiom, ![V_p, V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_p))))))).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (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,h4s_nums_suc(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,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
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_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_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_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_numerals_numeralu_u_addu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_NOTu_u_LEQ, axiom, ![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,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_RIGHTu_u_ADDu_u_DISTRIB, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,V_p))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_MULTu_u_LEFTu_u_1, 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_ADDu_u_ASSOC, axiom, ![V_p, 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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,V_p)))).
fof(ah4s_arithmetics_ADDu_u_COMM, 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_LESSu_u_EQ, axiom, ![V_n, V_m]: s(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_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_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_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(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_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(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_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_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_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_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_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_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
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_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_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_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_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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(ch4s_binaryu_u_ieees_floatu_u_nchotomy, conjecture, ![TV_u_27w,TV_u_27t]: ![V_ff]: ?[V_c, V_c0, V_c1]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_ff) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),h4s_binaryu_u_ieees_float0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_c0))),s(t_h4s_fcps_cart(t_bool,TV_u_27t),V_c1)))).
