%   ORIGINAL: h4/toto/toto__trans__less_c0
% 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/toto/totoLLtrans: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Goal: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
%   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_totos_totoLLtrans]: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Goal: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
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_Q251342,TV_Q251338]: ![V_f, V_g]: (![V_x]: s(TV_Q251338,happ(s(t_fun(TV_Q251342,TV_Q251338),V_f),s(TV_Q251342,V_x))) = s(TV_Q251338,happ(s(t_fun(TV_Q251342,TV_Q251338),V_g),s(TV_Q251342,V_x))) => s(t_fun(TV_Q251342,TV_Q251338),V_f) = s(t_fun(TV_Q251342,TV_Q251338),V_g))).
fof(ah4s_totos_totoLLtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ch4s_totos_totou_u_transu_u_lessu_c0, conjecture, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
