%   ORIGINAL: h4/integer/INT__LTE__ANTSYM
% 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/CONJ__SYM: !t2 t1. t1 /\ t2 <=> t2 /\ t1
% Assm: h4/integer/INT__LET__ANTISYM: !y x. ~(h4/integer/int__lt x y /\ h4/integer/int__le y x)
% Goal: !y x. ~(h4/integer/int__le x y /\ h4/integer/int__lt y x)
%   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_CONJu_u_SYM]: !t2 t1. t1 /\ t2 <=> t2 /\ t1
% Assm [h4s_integers_INTu_u_LETu_u_ANTISYM]: !y x. ~(h4/integer/int__lt x y /\ h4/integer/int__le y x)
% Goal: !y x. ~(h4/integer/int__le x y /\ h4/integer/int__lt y x)
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_Q2875,TV_Q2871]: ![V_f, V_g]: (![V_x]: s(TV_Q2871,happ(s(t_fun(TV_Q2875,TV_Q2871),V_f),s(TV_Q2875,V_x))) = s(TV_Q2871,happ(s(t_fun(TV_Q2875,TV_Q2871),V_g),s(TV_Q2875,V_x))) => s(t_fun(TV_Q2875,TV_Q2871),V_f) = s(t_fun(TV_Q2875,TV_Q2871),V_g))).
fof(ah4s_bools_CONJu_u_SYM, 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))))).
fof(ah4s_integers_INTu_u_LETu_u_ANTISYM, axiom, ![V_y, V_x]: ~ ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x))))))).
fof(ch4s_integers_INTu_u_LTEu_u_ANTSYM, conjecture, ![V_y, V_x]: ~ ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x))))))).
