%   ORIGINAL: h4/sorting/PERM__FUN__CONS__APPEND__2
% 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/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/list/APPEND0_c1: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm: h4/sorting/PERM__CONG: !L4 L3 L2 L1. h4/sorting/PERM L1 L3 /\ h4/sorting/PERM L2 L4 ==> h4/sorting/PERM (h4/list/APPEND L1 L2) (h4/list/APPEND L3 L4)
% Assm: h4/sorting/PERM__EQUIVALENCE__ALT__DEF: !y x. h4/sorting/PERM x y <=> h4/sorting/PERM x = h4/sorting/PERM y
% Assm: h4/sorting/PERM__FUN__APPEND__CONS: !x l2 l1. h4/sorting/PERM (h4/list/APPEND l1 (h4/list/CONS x l2)) = h4/sorting/PERM (h4/list/APPEND (h4/list/CONS x l1) l2)
% Goal: !x l2 l1 l. h4/sorting/PERM l1 = h4/sorting/PERM (h4/list/CONS x l2) ==> h4/sorting/PERM (h4/list/APPEND l l1) = h4/sorting/PERM (h4/list/CONS x (h4/list/APPEND l l2))
%   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_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm [h4s_sortings_PERMu_u_CONG]: !L4 L3 L2 L1. happ (h4/sorting/PERM L1) L3 /\ happ (h4/sorting/PERM L2) L4 ==> happ (h4/sorting/PERM (h4/list/APPEND L1 L2)) (h4/list/APPEND L3 L4)
% Assm [h4s_sortings_PERMu_u_EQUIVALENCEu_u_ALTu_u_DEF]: !y x. happ (h4/sorting/PERM x) y <=> h4/sorting/PERM x = h4/sorting/PERM y
% Assm [h4s_sortings_PERMu_u_FUNu_u_APPENDu_u_CONS]: !x l2 l1. h4/sorting/PERM (h4/list/APPEND l1 (h4/list/CONS x l2)) = h4/sorting/PERM (h4/list/APPEND (h4/list/CONS x l1) l2)
% Goal: !x l2 l1 l. h4/sorting/PERM l1 = h4/sorting/PERM (h4/list/CONS x l2) ==> h4/sorting/PERM (h4/list/APPEND l l1) = h4/sorting/PERM (h4/list/CONS x (h4/list/APPEND l l2))
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_Q276834,TV_Q276830]: ![V_f, V_g]: (![V_x]: s(TV_Q276830,happ(s(t_fun(TV_Q276834,TV_Q276830),V_f),s(TV_Q276834,V_x))) = s(TV_Q276830,happ(s(t_fun(TV_Q276834,TV_Q276830),V_g),s(TV_Q276834,V_x))) => s(t_fun(TV_Q276834,TV_Q276830),V_f) = s(t_fun(TV_Q276834,TV_Q276830),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_IMPu_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_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_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_lists_APPEND0u_c1, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_sortings_PERMu_u_CONG, axiom, ![TV_u_27a]: ![V_L4, V_L3, V_L2, V_L1]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),V_L1))),s(t_h4s_lists_list(TV_u_27a),V_L3)))) & p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),V_L2))),s(t_h4s_lists_list(TV_u_27a),V_L4))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_L1),s(t_h4s_lists_list(TV_u_27a),V_L2))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_L3),s(t_h4s_lists_list(TV_u_27a),V_L4)))))))).
fof(ah4s_sortings_PERMu_u_EQUIVALENCEu_u_ALTu_u_DEF, axiom, ![TV_u_27a]: ![V_y, V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),V_x))),s(t_h4s_lists_list(TV_u_27a),V_y)))) <=> s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),V_x))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),V_y))))).
fof(ah4s_sortings_PERMu_u_FUNu_u_APPENDu_u_CONS, axiom, ![TV_u_27a]: ![V_x, V_l2, V_l1]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l2))))))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ch4s_sortings_PERMu_u_FUNu_u_CONSu_u_APPENDu_u_2, conjecture, ![TV_u_27a]: ![V_x, V_l2, V_l1, V_l]: (s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l2))))) => s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_l1))))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_l2))))))))).
