%   ORIGINAL: h4/inftree/inftree__nchotomy
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> 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/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/EXISTS__REFL: !a. ?x. x = a
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/inftree/inftree__11_c0: !a2 a1. h4/inftree/iLf a1 = h4/inftree/iLf a2 <=> a1 = a2
% Assm: h4/inftree/inftree__11_c1: !f2 f1 b2 b1. h4/inftree/iNd b1 f1 = h4/inftree/iNd b2 f2 <=> b1 = b2 /\ f1 = f2
% Assm: h4/inftree/inftree__distinct: !f b a. ~(h4/inftree/iLf a = h4/inftree/iNd b f)
% Assm: h4/inftree/inftree__ind: !P. (!a. P (h4/inftree/iLf a)) /\ (!b f. (!d. P (f d)) ==> P (h4/inftree/iNd b f)) ==> (!t. P t)
% Goal: !t. (?a. t = h4/inftree/iLf a) \/ (?b d. t = h4/inftree/iNd b d)
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> 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_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_EXISTSu_u_REFL]: !a. ?x. x = a
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_inftrees_inftreeu_u_11u_c0]: !a2 a1. h4/inftree/iLf a1 = h4/inftree/iLf a2 <=> a1 = a2
% Assm [h4s_inftrees_inftreeu_u_11u_c1]: !f2 f1 b2 b1. h4/inftree/iNd b1 f1 = h4/inftree/iNd b2 f2 <=> b1 = b2 /\ f1 = f2
% Assm [h4s_inftrees_inftreeu_u_distinct]: !f b a. ~(h4/inftree/iLf a = h4/inftree/iNd b f)
% Assm [h4s_inftrees_inftreeu_u_ind]: !P. (!a. happ P (h4/inftree/iLf a)) /\ (!b f. (!d. happ P (happ f d)) ==> happ P (h4/inftree/iNd b f)) ==> (!t. happ P t)
% Goal: !t. (?a. t = h4/inftree/iLf a) \/ (?b d. t = h4/inftree/iNd b d)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q299498,TV_Q299494]: ![V_f, V_g]: (![V_x]: s(TV_Q299494,happ(s(t_fun(TV_Q299498,TV_Q299494),V_f),s(TV_Q299498,V_x))) = s(TV_Q299494,happ(s(t_fun(TV_Q299498,TV_Q299494),V_g),s(TV_Q299498,V_x))) => s(t_fun(TV_Q299498,TV_Q299494),V_f) = s(t_fun(TV_Q299498,TV_Q299494),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXISTSu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (?[V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t0))) <=> p(s(t_bool,t0)))).
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,t0) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_EXISTSu_u_REFL, axiom, ![TV_u_27a]: ![V_a]: ?[V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_a)).
fof(ah4s_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_inftrees_inftreeu_u_11u_c0, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_a2, V_a1]: (s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),h4s_inftrees_ilf(s(TV_u_27a,V_a1))) = s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),h4s_inftrees_ilf(s(TV_u_27a,V_a2))) <=> s(TV_u_27a,V_a1) = s(TV_u_27a,V_a2))).
fof(ah4s_inftrees_inftreeu_u_11u_c1, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_f2, V_f1, V_b2, V_b1]: (s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),h4s_inftrees_ind(s(TV_u_27b,V_b1),s(t_fun(TV_u_27c,t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c)),V_f1))) = s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),h4s_inftrees_ind(s(TV_u_27b,V_b2),s(t_fun(TV_u_27c,t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c)),V_f2))) <=> (s(TV_u_27b,V_b1) = s(TV_u_27b,V_b2) & s(t_fun(TV_u_27c,t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c)),V_f1) = s(t_fun(TV_u_27c,t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c)),V_f2)))).
fof(ah4s_inftrees_inftreeu_u_distinct, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_f, V_b, V_a]: ~ (s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),h4s_inftrees_ilf(s(TV_u_27a,V_a))) = s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),h4s_inftrees_ind(s(TV_u_27b,V_b),s(t_fun(TV_u_27c,t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c)),V_f))))).
fof(ah4s_inftrees_inftreeu_u_ind, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_P]: ((![V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),t_bool),V_P),s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),h4s_inftrees_ilf(s(TV_u_27a,V_a)))))) & ![V_b, V_f]: (![V_d]: p(s(t_bool,happ(s(t_fun(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),t_bool),V_P),s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27c,t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c)),V_f),s(TV_u_27c,V_d)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),t_bool),V_P),s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),h4s_inftrees_ind(s(TV_u_27b,V_b),s(t_fun(TV_u_27c,t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c)),V_f)))))))) => ![V_t]: p(s(t_bool,happ(s(t_fun(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),t_bool),V_P),s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),V_t)))))).
fof(ch4s_inftrees_inftreeu_u_nchotomy, conjecture, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_t]: (?[V_a]: s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),V_t) = s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),h4s_inftrees_ilf(s(TV_u_27a,V_a))) | ?[V_b, V_d]: s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),V_t) = s(t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c),h4s_inftrees_ind(s(TV_u_27b,V_b),s(t_fun(TV_u_27c,t_h4s_inftrees_inftree(TV_u_27a,TV_u_27b,TV_u_27c)),V_d))))).
