%   ORIGINAL: h4/poly/POLY__NEG__CLAUSES_c1
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/real/REAL__MUL__LID: !x. h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm: h4/real/REAL__MUL__LNEG: !y x. h4/realax/real__mul (h4/realax/real__neg x) y = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm: h4/poly/poly__neg__def: h4/poly/poly__neg = h4/poly/_23_23 (h4/realax/real__neg (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/poly/POLY__CMUL__CLAUSES_c0: !c. h4/poly/_23_23 c h4/list/NIL = h4/list/NIL
% Assm: h4/poly/POLY__CMUL__CLAUSES_c1: !t h c. h4/poly/_23_23 c (h4/list/CONS h t) = h4/list/CONS (h4/realax/real__mul c h) (h4/poly/_23_23 c t)
% Goal: !t h. h4/poly/poly__neg (h4/list/CONS h t) = h4/list/CONS (h4/realax/real__neg h) (h4/poly/poly__neg t)
%   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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_reals_REALu_u_MULu_u_LID]: !x. h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm [h4s_reals_REALu_u_MULu_u_LNEG]: !y x. h4/realax/real__mul (h4/realax/real__neg x) y = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm [h4s_polys_polyu_u_negu_u_def]: h4/poly/poly__neg = h4/poly/_23_23 (h4/realax/real__neg (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_polys_POLYu_u_CMULu_u_CLAUSESu_c0]: !c. happ (h4/poly/_23_23 c) h4/list/NIL = h4/list/NIL
% Assm [h4s_polys_POLYu_u_CMULu_u_CLAUSESu_c1]: !t h c. happ (h4/poly/_23_23 c) (h4/list/CONS h t) = h4/list/CONS (h4/realax/real__mul c h) (happ (h4/poly/_23_23 c) t)
% Goal: !t h. happ h4/poly/poly__neg (h4/list/CONS h t) = h4/list/CONS (h4/realax/real__neg h) (happ h4/poly/poly__neg t)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q213861,TV_Q213857]: ![V_f, V_g]: (![V_x]: s(TV_Q213857,happ(s(t_fun(TV_Q213861,TV_Q213857),V_f),s(TV_Q213861,V_x))) = s(TV_Q213857,happ(s(t_fun(TV_Q213861,TV_Q213857),V_g),s(TV_Q213861,V_x))) => s(t_fun(TV_Q213861,TV_Q213857),V_f) = s(t_fun(TV_Q213861,TV_Q213857),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t0)))).
fof(ah4s_reals_REALu_u_MULu_u_LID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_reals_REALu_u_MULu_u_LNEG, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_polys_polyu_u_negu_u_def, axiom, s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),h4s_polys_polyu_u_neg) = s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))).
fof(ah4s_polys_POLYu_u_CMULu_u_CLAUSESu_c0, axiom, ![V_c]: s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,V_c))),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)).
fof(ah4s_polys_POLYu_u_CMULu_u_CLAUSESu_c1, axiom, ![V_t, V_h, V_c]: s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,V_c))),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_cons(s(t_h4s_realaxs_real,V_h),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t))))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_cons(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_c),s(t_h4s_realaxs_real,V_h))),s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,V_c))),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t)))))).
fof(ch4s_polys_POLYu_u_NEGu_u_CLAUSESu_c1, conjecture, ![V_t, V_h]: s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),h4s_polys_polyu_u_neg),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_cons(s(t_h4s_realaxs_real,V_h),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t))))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_cons(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_h))),s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),h4s_polys_polyu_u_neg),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t)))))).
