%   ORIGINAL: h4/integer/INT__MOD__CALCULATE_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/integer/INT__MOD__NEG: !q p. ~(q = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__mod p (h4/integer/int__neg q) = h4/integer/int__neg (h4/integer/int__mod (h4/integer/int__neg p) q)
% Goal: !q p. ~(q = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__mod p (h4/integer/int__neg q) = h4/integer/int__neg (h4/integer/int__mod (h4/integer/int__neg p) q)
%   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_integers_INTu_u_MODu_u_NEG]: !q p. ~(q = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__mod p (h4/integer/int__neg q) = h4/integer/int__neg (h4/integer/int__mod (h4/integer/int__neg p) q)
% Goal: !q p. ~(q = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__mod p (h4/integer/int__neg q) = h4/integer/int__neg (h4/integer/int__mod (h4/integer/int__neg p) q)
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_Q9727,TV_Q9723]: ![V_f, V_g]: (![V_x]: s(TV_Q9723,happ(s(t_fun(TV_Q9727,TV_Q9723),V_f),s(TV_Q9727,V_x))) = s(TV_Q9723,happ(s(t_fun(TV_Q9727,TV_Q9723),V_g),s(TV_Q9727,V_x))) => s(t_fun(TV_Q9727,TV_Q9723),V_f) = s(t_fun(TV_Q9727,TV_Q9723),V_g))).
fof(ah4s_integers_INTu_u_MODu_u_NEG, axiom, ![V_q, V_p]: (~ (s(t_h4s_integers_int,V_q) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_q))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_p))),s(t_h4s_integers_int,V_q))))))).
fof(ch4s_integers_INTu_u_MODu_u_CALCULATEu_c1, conjecture, ![V_q, V_p]: (~ (s(t_h4s_integers_int,V_q) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_q))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_p))),s(t_h4s_integers_int,V_q))))))).
