%   ORIGINAL: h4/sorting/PERM__FUN__CONS__11__SWAP__AT__FRONT
% 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/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/sorting/PERM__CONS__IFF: !x l2 l1. h4/sorting/PERM (h4/list/CONS x l1) (h4/list/CONS x l2) <=> h4/sorting/PERM l1 l2
% 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__SWAP__AT__FRONT: !y x l. h4/sorting/PERM (h4/list/CONS x (h4/list/CONS y l)) = h4/sorting/PERM (h4/list/CONS y (h4/list/CONS x l))
% Goal: !y x l2 l1. h4/sorting/PERM l1 = h4/sorting/PERM (h4/list/CONS x l2) ==> h4/sorting/PERM (h4/list/CONS y l1) = h4/sorting/PERM (h4/list/CONS x (h4/list/CONS y 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_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_sortings_PERMu_u_CONSu_u_IFF]: !x l2 l1. happ (h4/sorting/PERM (h4/list/CONS x l1)) (h4/list/CONS x l2) <=> happ (h4/sorting/PERM l1) l2
% 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_SWAPu_u_ATu_u_FRONT]: !y x l. h4/sorting/PERM (h4/list/CONS x (h4/list/CONS y l)) = h4/sorting/PERM (h4/list/CONS y (h4/list/CONS x l))
% Goal: !y x l2 l1. h4/sorting/PERM l1 = h4/sorting/PERM (h4/list/CONS x l2) ==> h4/sorting/PERM (h4/list/CONS y l1) = h4/sorting/PERM (h4/list/CONS x (h4/list/CONS y 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_Q276759,TV_Q276755]: ![V_f, V_g]: (![V_x]: s(TV_Q276755,happ(s(t_fun(TV_Q276759,TV_Q276755),V_f),s(TV_Q276759,V_x))) = s(TV_Q276755,happ(s(t_fun(TV_Q276759,TV_Q276755),V_g),s(TV_Q276759,V_x))) => s(t_fun(TV_Q276759,TV_Q276755),V_f) = s(t_fun(TV_Q276759,TV_Q276755),V_g))).
fof(ah4s_bools_TRUTH, axiom, 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_sortings_PERMu_u_CONSu_u_IFF, axiom, ![TV_u_27a]: ![V_x, V_l2, V_l1]: 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_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),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l2))))) = 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_l2)))).
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_SWAPu_u_ATu_u_FRONT, axiom, ![TV_u_27a]: ![V_y, V_x, 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),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),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),h4s_lists_cons(s(TV_u_27a,V_y),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_l)))))))).
fof(ch4s_sortings_PERMu_u_FUNu_u_CONSu_u_11u_u_SWAPu_u_ATu_u_FRONT, conjecture, ![TV_u_27a]: ![V_y, 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),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_cons(s(TV_u_27a,V_y),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_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_l2))))))))).
