%   ORIGINAL: h4/poly/POLY__MUL__CLAUSES_c0
% 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/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> 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/list/NOT__CONS__NIL: !a1 a0. ~(h4/list/CONS a0 a1 = h4/list/NIL)
% Assm: h4/poly/poly__mul__def_c0: !l2. h4/poly/poly__mul h4/list/NIL l2 = h4/list/NIL
% Assm: h4/poly/poly__mul__def_c1: !t l2 h. h4/poly/poly__mul (h4/list/CONS h t) l2 = h4/bool/COND (t = h4/list/NIL) (h4/poly/_23_23 h l2) (h4/poly/poly__add (h4/poly/_23_23 h l2) (h4/list/CONS (h4/real/real__of__num h4/num/0) (h4/poly/poly__mul t l2)))
% Goal: !p2. h4/poly/poly__mul h4/list/NIL p2 = h4/list/NIL
%   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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> 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_lists_NOTu_u_CONSu_u_NIL]: !a1 a0. ~(h4/list/CONS a0 a1 = h4/list/NIL)
% Assm [h4s_polys_polyu_u_mulu_u_defu_c0]: !l2. h4/poly/poly__mul h4/list/NIL l2 = h4/list/NIL
% Assm [h4s_polys_polyu_u_mulu_u_defu_c1]: !t l2 h. ?v. (v <=> t = h4/list/NIL) /\ h4/poly/poly__mul (h4/list/CONS h t) l2 = h4/bool/COND v (h4/poly/_23_23 h l2) (h4/poly/poly__add (h4/poly/_23_23 h l2) (h4/list/CONS (h4/real/real__of__num h4/num/0) (h4/poly/poly__mul t l2)))
% Goal: !p2. h4/poly/poly__mul h4/list/NIL p2 = h4/list/NIL
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_Q213886,TV_Q213882]: ![V_f, V_g]: (![V_x]: s(TV_Q213882,happ(s(t_fun(TV_Q213886,TV_Q213882),V_f),s(TV_Q213886,V_x))) = s(TV_Q213882,happ(s(t_fun(TV_Q213886,TV_Q213882),V_g),s(TV_Q213886,V_x))) => s(t_fun(TV_Q213886,TV_Q213882),V_f) = s(t_fun(TV_Q213886,TV_Q213882),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_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_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_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_lists_NOTu_u_CONSu_u_NIL, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_polys_polyu_u_mulu_u_defu_c0, axiom, ![V_l2]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_mul(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)).
fof(ah4s_polys_polyu_u_mulu_u_defu_c1, axiom, ![V_t, V_l2, V_h]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_lists_list(t_h4s_realaxs_real),V_t) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)) & s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_mul(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),V_l2))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,V_h),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_add(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,V_h),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_cons(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_mul(s(t_h4s_lists_list(t_h4s_realaxs_real),V_t),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))))))))))).
fof(ch4s_polys_POLYu_u_MULu_u_CLAUSESu_c0, conjecture, ![V_p2]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_mul(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_realaxs_real),V_p2))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)).
