%   ORIGINAL: h4/sorting/PERM__EQUIVALENCE__ALT__DEF
% 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/relation/ALT__equivalence: !R. h4/relation/equivalence R <=> (!x y. R x y <=> R x = R y)
% Assm: h4/sorting/PERM__EQUIVALENCE: h4/relation/equivalence h4/sorting/PERM
% Goal: !y x. h4/sorting/PERM x y <=> h4/sorting/PERM x = h4/sorting/PERM y
%   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_relations_ALTu_u_equivalence]: !R. h4/relation/equivalence R <=> (!x y. happ (happ R x) y <=> happ R x = happ R y)
% Assm [h4s_sortings_PERMu_u_EQUIVALENCE]: h4/relation/equivalence h4/sorting/PERM
% Goal: !y x. happ (happ h4/sorting/PERM x) y <=> happ h4/sorting/PERM x = happ h4/sorting/PERM y
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_Q276081,TV_Q276077]: ![V_f, V_g]: (![V_x]: s(TV_Q276077,happ(s(t_fun(TV_Q276081,TV_Q276077),V_f),s(TV_Q276081,V_x))) = s(TV_Q276077,happ(s(t_fun(TV_Q276081,TV_Q276077),V_g),s(TV_Q276081,V_x))) => s(t_fun(TV_Q276081,TV_Q276077),V_f) = s(t_fun(TV_Q276081,TV_Q276077),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_relations_ALTu_u_equivalence, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_equivalence(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) <=> ![V_x, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) <=> s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y)))))).
fof(ah4s_sortings_PERMu_u_EQUIVALENCE, axiom, ![TV_u_27a]: p(s(t_bool,h4s_relations_equivalence(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),h4s_sortings_perm))))).
fof(ch4s_sortings_PERMu_u_EQUIVALENCEu_u_ALTu_u_DEF, conjecture, ![TV_u_27a]: ![V_y, V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),h4s_sortings_perm),s(t_h4s_lists_list(TV_u_27a),V_y))))).
