%   ORIGINAL: h4/binary__ieee/float__round__non__zero
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/words/n2w__11: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% 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_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_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_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_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/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__round__def: !toneg r mode. h4/binary__ieee/float__round mode toneg r = h4/bool/LET (\x. h4/bool/COND (h4/binary__ieee/float__is__zero x) (h4/bool/COND toneg (h4/binary__ieee/float__minus__zero h4/bool/the__value) (h4/binary__ieee/float__plus__zero h4/bool/the__value)) x) (h4/binary__ieee/round mode r)
% Assm: h4/binary__ieee/float__is__zero0: !x. h4/binary__ieee/float__is__zero x <=> h4/binary__ieee/float__Exponent x = h4/words/n2w h4/num/0 /\ h4/binary__ieee/float__Significand x = h4/words/n2w h4/num/0
% Goal: !toneg s r mode f e. h4/binary__ieee/round mode r = h4/binary__ieee/float__Sign__fupd (h4/combin/K s) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K e) (h4/binary__ieee/float__Significand__fupd (h4/combin/K f) h4/bool/ARB)) /\ (~(e = h4/words/n2w h4/num/0) \/ ~(f = h4/words/n2w h4/num/0)) ==> h4/binary__ieee/float__round mode toneg r = h4/binary__ieee/float__Sign__fupd (h4/combin/K s) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K e) (h4/binary__ieee/float__Significand__fupd (h4/combin/K f) h4/bool/ARB))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_combins_Ku_u_THM]: !y x. happ (h4/combin/K x) y = x
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_wordss_n2wu_u_11]: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c2]: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Exponent f
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c4]: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Significand f
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c5]: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Exponent__fupd f0 f) = h4/binary__ieee/float__Significand f
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c7]: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Exponent__fupd f0 f) = happ f0 (h4/binary__ieee/float__Exponent f)
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c8]: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Significand__fupd f0 f) = happ f0 (h4/binary__ieee/float__Significand f)
% Assm [h4s_binaryu_u_ieees_floatu_u_literalu_u_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 [h4s_binaryu_u_ieees_floatu_u_roundu_u_def]: !_0. (!toneg x. happ (happ _0 toneg) x = h4/bool/COND (h4/binary__ieee/float__is__zero x) (h4/bool/COND toneg (h4/binary__ieee/float__minus__zero h4/bool/the__value) (h4/binary__ieee/float__plus__zero h4/bool/the__value)) x) ==> (!toneg r mode. h4/binary__ieee/float__round mode toneg r = h4/bool/LET (happ _0 toneg) (h4/binary__ieee/round mode r))
% Assm [h4s_binaryu_u_ieees_floatu_u_isu_u_zero0]: !x. h4/binary__ieee/float__is__zero x <=> h4/binary__ieee/float__Exponent x = h4/words/n2w h4/num/0 /\ h4/binary__ieee/float__Significand x = h4/words/n2w h4/num/0
% Goal: !toneg s r mode f e. h4/binary__ieee/round mode r = h4/binary__ieee/float__Sign__fupd (h4/combin/K s) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K e) (h4/binary__ieee/float__Significand__fupd (h4/combin/K f) h4/bool/ARB)) /\ (~(e = h4/words/n2w h4/num/0) \/ ~(f = h4/words/n2w h4/num/0)) ==> h4/binary__ieee/float__round mode toneg r = h4/binary__ieee/float__Sign__fupd (h4/combin/K s) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K e) (h4/binary__ieee/float__Significand__fupd (h4/combin/K f) h4/bool/ARB))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q108326,TV_Q108322]: ![V_f, V_g]: (![V_x]: s(TV_Q108322,happ(s(t_fun(TV_Q108326,TV_Q108322),V_f),s(TV_Q108326,V_x))) = s(TV_Q108322,happ(s(t_fun(TV_Q108326,TV_Q108322),V_g),s(TV_Q108326,V_x))) => s(t_fun(TV_Q108326,TV_Q108322),V_f) = s(t_fun(TV_Q108326,TV_Q108322),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f0)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
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_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f0))) <=> p(s(t_bool,f0)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f0)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f0)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f0)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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,f0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
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_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_wordss_n2wu_u_11, axiom, ![TV_u_27a]: ![V_n, V_m]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
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),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_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),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_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),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_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),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_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),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_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),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),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),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),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),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),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_roundu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_uu_0]: (![V_toneg, V_x]: 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)),happ(s(t_fun(t_bool,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))),V_uu_0),s(t_bool,V_toneg))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_zero(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_toneg),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) => ![V_toneg, V_r, V_mode]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_round(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_bool,V_toneg),s(t_h4s_realaxs_real,V_r))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_let(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)),happ(s(t_fun(t_bool,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))),V_uu_0),s(t_bool,V_toneg))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_round(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_h4s_realaxs_real,V_r))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_isu_u_zero0, axiom, ![TV_u_27b,TV_u_27a]: ![V_x]: (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_zero(s(t_h4s_binaryu_u_ieees_float(TV_u_27a,TV_u_27b),V_x)))) <=> (s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27a,TV_u_27b),V_x))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))) & s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27a,TV_u_27b),V_x))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ch4s_binaryu_u_ieees_floatu_u_roundu_u_nonu_u_zero, conjecture, ![TV_u_27b,TV_u_27a]: ![V_toneg, V_s, V_r, V_mode, V_f, V_e]: ((s(t_h4s_binaryu_u_ieees_float(TV_u_27b,TV_u_27a),h4s_binaryu_u_ieees_round(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_h4s_realaxs_real,V_r))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27b,TV_u_27a),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_s))),s(t_h4s_binaryu_u_ieees_float(TV_u_27b,TV_u_27a),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_e))),s(t_h4s_binaryu_u_ieees_float(TV_u_27b,TV_u_27a),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27b),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_f))),s(t_h4s_binaryu_u_ieees_float(TV_u_27b,TV_u_27a),h4s_bools_arb))))))) & (~ (s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_e) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) | ~ (s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_f) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))))) => s(t_h4s_binaryu_u_ieees_float(TV_u_27b,TV_u_27a),h4s_binaryu_u_ieees_floatu_u_round(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_bool,V_toneg),s(t_h4s_realaxs_real,V_r))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27b,TV_u_27a),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_s))),s(t_h4s_binaryu_u_ieees_float(TV_u_27b,TV_u_27a),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_e))),s(t_h4s_binaryu_u_ieees_float(TV_u_27b,TV_u_27a),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27b),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_f))),s(t_h4s_binaryu_u_ieees_float(TV_u_27b,TV_u_27a),h4s_bools_arb))))))))).
