%   ORIGINAL: h4/Omega/eval__step__extra2
% 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/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Goal: !x ups lows ex_27 ex. ((h4/Omega/evalupper x ups /\ h4/Omega/evallower x lows) /\ ex) /\ ex_27 <=> (h4/Omega/evalupper x ups /\ h4/Omega/evallower x lows) /\ ex /\ ex_27
%   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_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Goal: !x ups lows ex_27 ex. ((h4/Omega/evalupper x ups /\ h4/Omega/evallower x lows) /\ ex) /\ ex_27 <=> (h4/Omega/evalupper x ups /\ h4/Omega/evallower x lows) /\ ex /\ ex_27
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_Q19441,TV_Q19437]: ![V_f, V_g]: (![V_x]: s(TV_Q19437,happ(s(t_fun(TV_Q19441,TV_Q19437),V_f),s(TV_Q19441,V_x))) = s(TV_Q19437,happ(s(t_fun(TV_Q19441,TV_Q19437),V_g),s(TV_Q19441,V_x))) => s(t_fun(TV_Q19441,TV_Q19437),V_f) = s(t_fun(TV_Q19441,TV_Q19437),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
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(ch4s_Omegas_evalu_u_stepu_u_extra2, conjecture, ![V_x, V_ups, V_lows, V_exu_27, V_ex]: ((((p(s(t_bool,h4s_omegas_evalupper(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_ups)))) & p(s(t_bool,h4s_omegas_evallower(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lows))))) & p(s(t_bool,V_ex))) & p(s(t_bool,V_exu_27))) <=> ((p(s(t_bool,h4s_omegas_evalupper(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_ups)))) & p(s(t_bool,h4s_omegas_evallower(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lows))))) & (p(s(t_bool,V_ex)) & p(s(t_bool,V_exu_27)))))).
