%   ORIGINAL: h4/sorting/PERM__SINGLE__SWAP__REFL
% 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_c4: !t. t /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/list/APPEND__NIL: !l. h4/list/APPEND l h4/list/NIL = l
% Assm: h4/sorting/PERM__SINGLE__SWAP__DEF: !l2 l1. h4/sorting/PERM__SINGLE__SWAP l1 l2 <=> (?x1 x2 x3. l1 = h4/list/APPEND (h4/list/APPEND x1 x2) x3 /\ l2 = h4/list/APPEND (h4/list/APPEND x1 x3) x2)
% Goal: !l. h4/sorting/PERM__SINGLE__SWAP l l
%   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_c4]: !t. t /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_lists_APPENDu_u_NIL]: !l. h4/list/APPEND l h4/list/NIL = l
% Assm [h4s_sortings_PERMu_u_SINGLEu_u_SWAPu_u_DEF]: !l2 l1. h4/sorting/PERM__SINGLE__SWAP l1 l2 <=> (?x1 x2 x3. l1 = h4/list/APPEND (h4/list/APPEND x1 x2) x3 /\ l2 = h4/list/APPEND (h4/list/APPEND x1 x3) x2)
% Goal: !l. h4/sorting/PERM__SINGLE__SWAP l l
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_Q275831,TV_Q275827]: ![V_f, V_g]: (![V_x]: s(TV_Q275827,happ(s(t_fun(TV_Q275831,TV_Q275827),V_f),s(TV_Q275831,V_x))) = s(TV_Q275827,happ(s(t_fun(TV_Q275831,TV_Q275827),V_g),s(TV_Q275831,V_x))) => s(t_fun(TV_Q275831,TV_Q275827),V_f) = s(t_fun(TV_Q275831,TV_Q275827),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_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_lists_APPENDu_u_NIL, axiom, ![TV_u_27a]: ![V_l]: 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),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_sortings_PERMu_u_SINGLEu_u_SWAPu_u_DEF, axiom, ![TV_u_27a]: ![V_l2, V_l1]: (p(s(t_bool,h4s_sortings_permu_u_singleu_u_swap(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))) <=> ?[V_x1, V_x2, V_x3]: (s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_x1),s(t_h4s_lists_list(TV_u_27a),V_x2))),s(t_h4s_lists_list(TV_u_27a),V_x3))) & 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),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_x1),s(t_h4s_lists_list(TV_u_27a),V_x3))),s(t_h4s_lists_list(TV_u_27a),V_x2)))))).
fof(ch4s_sortings_PERMu_u_SINGLEu_u_SWAPu_u_REFL, conjecture, ![TV_u_27a]: ![V_l]: p(s(t_bool,h4s_sortings_permu_u_singleu_u_swap(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_l))))).
