%   ORIGINAL: h4/complex/COMPLEX__INV__NZ
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/complex/COMPLEX__INV__EQ__0: !z. h4/complex/complex__inv z = h4/complex/complex__of__num h4/num/0 <=> z = h4/complex/complex__of__num h4/num/0
% Goal: !z. ~(z = h4/complex/complex__of__num h4/num/0) ==> ~(h4/complex/complex__inv z = h4/complex/complex__of__num h4/num/0)
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_complexs_COMPLEXu_u_INVu_u_EQu_u_0]: !z. h4/complex/complex__inv z = h4/complex/complex__of__num h4/num/0 <=> z = h4/complex/complex__of__num h4/num/0
% Goal: !z. ~(z = h4/complex/complex__of__num h4/num/0) ==> ~(h4/complex/complex__inv z = h4/complex/complex__of__num h4/num/0)
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_Q257532,TV_Q257528]: ![V_f, V_g]: (![V_x]: s(TV_Q257528,happ(s(t_fun(TV_Q257532,TV_Q257528),V_f),s(TV_Q257532,V_x))) = s(TV_Q257528,happ(s(t_fun(TV_Q257532,TV_Q257528),V_g),s(TV_Q257532,V_x))) => s(t_fun(TV_Q257532,TV_Q257528),V_f) = s(t_fun(TV_Q257532,TV_Q257528),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_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_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_complexs_COMPLEXu_u_INVu_u_EQu_u_0, axiom, ![V_z]: (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ch4s_complexs_COMPLEXu_u_INVu_u_NZ, conjecture, ![V_z]: (~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => ~ (s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_inv(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
