%   ORIGINAL: h4/real/REAL__NEG__EQ
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/real/REAL__NEGNEG: !x. h4/realax/real__neg (h4/realax/real__neg x) = x
% Goal: !y x. h4/realax/real__neg x = y <=> x = h4/realax/real__neg 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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_reals_REALu_u_NEGNEG]: !x. h4/realax/real__neg (h4/realax/real__neg x) = x
% Goal: !y x. h4/realax/real__neg x = y <=> x = h4/realax/real__neg 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_Q62376,TV_Q62372]: ![V_f, V_g]: (![V_x]: s(TV_Q62372,happ(s(t_fun(TV_Q62376,TV_Q62372),V_f),s(TV_Q62376,V_x))) = s(TV_Q62372,happ(s(t_fun(TV_Q62376,TV_Q62372),V_g),s(TV_Q62376,V_x))) => s(t_fun(TV_Q62376,TV_Q62372),V_f) = s(t_fun(TV_Q62376,TV_Q62372),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_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_reals_REALu_u_NEGNEG, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,V_x)).
fof(ch4s_reals_REALu_u_NEGu_u_EQ, conjecture, ![V_y, V_x]: (s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_y) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y))))).
