%   ORIGINAL: h4/arithmetic/EXP__1_c0
% 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/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Assm: h4/arithmetic/EXP0_c0: !m. h4/arithmetic/EXP m h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/arithmetic/EXP0_c1: !n m. h4/arithmetic/EXP m (h4/num/SUC n) = h4/arithmetic/_2A m (h4/arithmetic/EXP m n)
% Assm: h4/arithmetic/ONE: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm: h4/arithmetic/MULT__CLAUSES_c3: !m. h4/arithmetic/_2A m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Assm: h4/arithmetic/MULT__EQ__1: !y x. h4/arithmetic/_2A x y = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) <=> x = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) /\ y = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Goal: !n. h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
%   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_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% Assm [h4s_arithmetics_EXP0u_c0]: !m. h4/arithmetic/EXP m h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_arithmetics_EXP0u_c1]: !n m. h4/arithmetic/EXP m (h4/num/SUC n) = h4/arithmetic/_2A m (h4/arithmetic/EXP m n)
% Assm [h4s_arithmetics_ONE]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c3]: !m. h4/arithmetic/_2A m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Assm [h4s_arithmetics_MULTu_u_EQu_u_1]: !y x. h4/arithmetic/_2A x y = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) <=> x = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) /\ y = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Goal: !n. h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
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_Q311423,TV_Q311419]: ![V_f, V_g]: (![V_x]: s(TV_Q311419,happ(s(t_fun(TV_Q311423,TV_Q311419),V_f),s(TV_Q311423,V_x))) = s(TV_Q311419,happ(s(t_fun(TV_Q311423,TV_Q311419),V_g),s(TV_Q311423,V_x))) => s(t_fun(TV_Q311423,TV_Q311419),V_f) = s(t_fun(TV_Q311423,TV_Q311419),V_g))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_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_nums_INDUCTION, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_EXP0u_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_arithmetics_EXP0u_c1, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ONE, axiom, s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c3, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_MULTu_u_EQu_u_1, axiom, ![V_y, V_x]: (s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))) <=> (s(t_h4s_nums_num,V_x) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))) & s(t_h4s_nums_num,V_y) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ch4s_arithmetics_EXPu_u_1u_c0, conjecture, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
