%   ORIGINAL: h4/sorting/PERM__EQUIVALENCE
% 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__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/relation/EQC__EQUIVALENCE: !R. h4/relation/equivalence (h4/relation/EQC R)
% Assm: h4/sorting/PERM__EQC: h4/sorting/PERM = h4/relation/EQC h4/sorting/PERM__SINGLE__SWAP
% Goal: h4/relation/equivalence h4/sorting/PERM
%   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_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_relations_EQCu_u_EQUIVALENCE]: !R. h4/relation/equivalence (h4/relation/EQC R)
% Assm [h4s_sortings_PERMu_u_EQC]: h4/sorting/PERM = h4/relation/EQC h4/sorting/PERM__SINGLE__SWAP
% Goal: h4/relation/equivalence h4/sorting/PERM
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_Q276056,TV_Q276052]: ![V_f, V_g]: (![V_x]: s(TV_Q276052,happ(s(t_fun(TV_Q276056,TV_Q276052),V_f),s(TV_Q276056,V_x))) = s(TV_Q276052,happ(s(t_fun(TV_Q276056,TV_Q276052),V_g),s(TV_Q276056,V_x))) => s(t_fun(TV_Q276056,TV_Q276052),V_f) = s(t_fun(TV_Q276056,TV_Q276052),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_EQCu_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)),h4s_relations_eqc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))))))).
fof(ah4s_sortings_PERMu_u_EQC, axiom, ![TV_u_27a]: 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_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),h4s_relations_eqc(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),h4s_sortings_permu_u_singleu_u_swap)))).
fof(ch4s_sortings_PERMu_u_EQUIVALENCE, conjecture, ![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))))).
