%   ORIGINAL: h4/numpair/npair0
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/numpair/nfst__npair: !y x. h4/numpair/nfst (h4/numpair/npair x y) = x
% Assm: h4/numpair/nsnd__npair: !y x. h4/numpair/nsnd (h4/numpair/npair x y) = y
% Assm: h4/numpair/npair__cases: !n. ?x y. n = h4/numpair/npair x y
% Goal: !n. h4/numpair/npair (h4/numpair/nfst n) (h4/numpair/nsnd n) = n
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_numpairs_nfstu_u_npair]: !y x. h4/numpair/nfst (h4/numpair/npair x y) = x
% Assm [h4s_numpairs_nsndu_u_npair]: !y x. h4/numpair/nsnd (h4/numpair/npair x y) = y
% Assm [h4s_numpairs_npairu_u_cases]: !n. ?x y. n = h4/numpair/npair x y
% Goal: !n. h4/numpair/npair (h4/numpair/nfst n) (h4/numpair/nsnd n) = n
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_Q144635,TV_Q144631]: ![V_f, V_g]: (![V_x]: s(TV_Q144631,happ(s(t_fun(TV_Q144635,TV_Q144631),V_f),s(TV_Q144635,V_x))) = s(TV_Q144631,happ(s(t_fun(TV_Q144635,TV_Q144631),V_g),s(TV_Q144635,V_x))) => s(t_fun(TV_Q144635,TV_Q144631),V_f) = s(t_fun(TV_Q144635,TV_Q144631),V_g))).
fof(ah4s_bools_TRUTH, axiom, 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_numpairs_nfstu_u_npair, axiom, ![V_y, V_x]: s(t_h4s_nums_num,h4s_numpairs_nfst(s(t_h4s_nums_num,h4s_numpairs_npair(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_numpairs_nsndu_u_npair, axiom, ![V_y, V_x]: s(t_h4s_nums_num,h4s_numpairs_nsnd(s(t_h4s_nums_num,h4s_numpairs_npair(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))))) = s(t_h4s_nums_num,V_y)).
fof(ah4s_numpairs_npairu_u_cases, axiom, ![V_n]: ?[V_x, V_y]: s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_numpairs_npair(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y)))).
fof(ch4s_numpairs_npair0, conjecture, ![V_n]: s(t_h4s_nums_num,h4s_numpairs_npair(s(t_h4s_nums_num,h4s_numpairs_nfst(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_numpairs_nsnd(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
