%   ORIGINAL: h4/toto/totoEEtrans_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/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/toto/toto__equal__eq: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> x = y
% Goal: !z y x c. h4/toto/apto c x y = h4/toto/EQUAL /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/EQUAL
%   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_totos_totou_u_equalu_u_eq]: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> x = y
% Goal: !z y x c. h4/toto/apto c x y = h4/toto/EQUAL /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/EQUAL
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_Q251142,TV_Q251138]: ![V_f, V_g]: (![V_x]: s(TV_Q251138,happ(s(t_fun(TV_Q251142,TV_Q251138),V_f),s(TV_Q251142,V_x))) = s(TV_Q251138,happ(s(t_fun(TV_Q251142,TV_Q251138),V_g),s(TV_Q251142,V_x))) => s(t_fun(TV_Q251142,TV_Q251138),V_f) = s(t_fun(TV_Q251142,TV_Q251138),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_totos_totou_u_equalu_u_eq, axiom, ![TV_u_27a]: ![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_equal) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ch4s_totos_totoEEtransu_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_equal) & 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_equal)) => 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_equal))).
