%   ORIGINAL: h4/pred__set/pair__to__num__inv_c1
% 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_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% 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/pred__set/num__to__pair__def: !n. h4/pred__set/num__to__pair n = h4/pair/_2C (h4/numpair/nfst n) (h4/numpair/nsnd n)
% Assm: h4/pred__set/pair__to__num__def: !n m. h4/pred__set/pair__to__num (h4/pair/_2C m n) = h4/numpair/npair m n
% Goal: !y x. h4/pred__set/num__to__pair (h4/pred__set/pair__to__num (h4/pair/_2C x y)) = h4/pair/_2C x 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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_pairs_CLOSEDu_u_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% 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_predu_u_sets_numu_u_tou_u_pairu_u_def]: !n. h4/pred__set/num__to__pair n = h4/pair/_2C (h4/numpair/nfst n) (h4/numpair/nsnd n)
% Assm [h4s_predu_u_sets_pairu_u_tou_u_numu_u_def]: !n m. h4/pred__set/pair__to__num (h4/pair/_2C m n) = h4/numpair/npair m n
% Goal: !y x. h4/pred__set/num__to__pair (h4/pred__set/pair__to__num (h4/pair/_2C x y)) = h4/pair/_2C x 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_Q156527,TV_Q156523]: ![V_f, V_g]: (![V_x]: s(TV_Q156523,happ(s(t_fun(TV_Q156527,TV_Q156523),V_f),s(TV_Q156527,V_x))) = s(TV_Q156523,happ(s(t_fun(TV_Q156527,TV_Q156523),V_g),s(TV_Q156527,V_x))) => s(t_fun(TV_Q156527,TV_Q156523),V_f) = s(t_fun(TV_Q156527,TV_Q156523),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,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_pairs_CLOSEDu_u_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
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_predu_u_sets_numu_u_tou_u_pairu_u_def, axiom, ![V_n]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_predu_u_sets_numu_u_tou_u_pair(s(t_h4s_nums_num,V_n))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(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)))))).
fof(ah4s_predu_u_sets_pairu_u_tou_u_numu_u_def, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_predu_u_sets_pairu_u_tou_u_num(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_numpairs_npair(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ch4s_predu_u_sets_pairu_u_tou_u_numu_u_invu_c1, conjecture, ![V_y, V_x]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_predu_u_sets_numu_u_tou_u_pair(s(t_h4s_nums_num,h4s_predu_u_sets_pairu_u_tou_u_num(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))))))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y)))).
