%   ORIGINAL: h4/realax/TREAL__INV__0
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/realax/treal__00: h4/realax/treal__0 = h4/pair/_2C h4/hreal/hreal__1 h4/hreal/hreal__1
% Assm: h4/realax/treal__inv0: !y x. h4/realax/treal__inv (h4/pair/_2C x y) = h4/bool/COND (x = y) h4/realax/treal__0 (h4/bool/COND (h4/hreal/hreal__lt y x) (h4/pair/_2C (h4/hreal/hreal__add (h4/hreal/hreal__inv (h4/hreal/hreal__sub x y)) h4/hreal/hreal__1) h4/hreal/hreal__1) (h4/pair/_2C h4/hreal/hreal__1 (h4/hreal/hreal__add (h4/hreal/hreal__inv (h4/hreal/hreal__sub y x)) h4/hreal/hreal__1)))
% Assm: h4/realax/treal__eq0: !y2 y1 x2 x1. h4/realax/treal__eq (h4/pair/_2C x1 y1) (h4/pair/_2C x2 y2) <=> h4/hreal/hreal__add x1 y2 = h4/hreal/hreal__add x2 y1
% Goal: h4/realax/treal__eq (h4/realax/treal__inv h4/realax/treal__0) h4/realax/treal__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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_realaxs_trealu_u_00]: h4/realax/treal__0 = h4/pair/_2C h4/hreal/hreal__1 h4/hreal/hreal__1
% Assm [h4s_realaxs_trealu_u_inv0]: !y x. ?v. (v <=> x = y) /\ h4/realax/treal__inv (h4/pair/_2C x y) = h4/bool/COND v h4/realax/treal__0 (h4/bool/COND (h4/hreal/hreal__lt y x) (h4/pair/_2C (h4/hreal/hreal__add (h4/hreal/hreal__inv (h4/hreal/hreal__sub x y)) h4/hreal/hreal__1) h4/hreal/hreal__1) (h4/pair/_2C h4/hreal/hreal__1 (h4/hreal/hreal__add (h4/hreal/hreal__inv (h4/hreal/hreal__sub y x)) h4/hreal/hreal__1)))
% Assm [h4s_realaxs_trealu_u_eq0]: !y2 y1 x2 x1. h4/realax/treal__eq (h4/pair/_2C x1 y1) (h4/pair/_2C x2 y2) <=> h4/hreal/hreal__add x1 y2 = h4/hreal/hreal__add x2 y1
% Goal: h4/realax/treal__eq (h4/realax/treal__inv h4/realax/treal__0) h4/realax/treal__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_Q328739,TV_Q328735]: ![V_f, V_g]: (![V_x]: s(TV_Q328735,happ(s(t_fun(TV_Q328739,TV_Q328735),V_f),s(TV_Q328739,V_x))) = s(TV_Q328735,happ(s(t_fun(TV_Q328739,TV_Q328735),V_g),s(TV_Q328739,V_x))) => s(t_fun(TV_Q328739,TV_Q328735),V_f) = s(t_fun(TV_Q328739,TV_Q328735),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_realaxs_trealu_u_00, axiom, s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0) = s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1)))).
fof(ah4s_realaxs_trealu_u_inv0, axiom, ![V_y, V_x]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_hreals_hreal,V_x) = s(t_h4s_hreals_hreal,V_y)) & s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_inv(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))))) = s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_bools_cond(s(t_bool,h4s_hreals_hrealu_u_lt(s(t_h4s_hreals_hreal,V_y),s(t_h4s_hreals_hreal,V_x))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_inv(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_sub(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_inv(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_sub(s(t_h4s_hreals_hreal,V_y),s(t_h4s_hreals_hreal,V_x))))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1))))))))))).
fof(ah4s_realaxs_trealu_u_eq0, axiom, ![V_y2, V_y1, V_x2, V_x1]: (p(s(t_bool,h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,V_x1),s(t_h4s_hreals_hreal,V_y1))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_pairs_u_2c(s(t_h4s_hreals_hreal,V_x2),s(t_h4s_hreals_hreal,V_y2)))))) <=> s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x1),s(t_h4s_hreals_hreal,V_y2))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x2),s(t_h4s_hreals_hreal,V_y1))))).
fof(ch4s_realaxs_TREALu_u_INVu_u_0, conjecture, p(s(t_bool,h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_inv(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0))))).
