%   ORIGINAL: h4/toto/toto__glneq_c1
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/toto/all__cpn__distinct_c5: ~(h4/toto/GREATER = h4/toto/EQUAL)
% Assm: h4/toto/toto__equal__eq: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> x = y
% Goal: !y x c. h4/toto/apto c x y = h4/toto/GREATER ==> ~(x = y)
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_totos_allu_u_cpnu_u_distinctu_c5]: ~(h4/toto/GREATER = h4/toto/EQUAL)
% Assm [h4s_totos_totou_u_equalu_u_eq]: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> x = y
% Goal: !y x c. h4/toto/apto c x y = h4/toto/GREATER ==> ~(x = y)
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_Q251017,TV_Q251013]: ![V_f, V_g]: (![V_x]: s(TV_Q251013,happ(s(t_fun(TV_Q251017,TV_Q251013),V_f),s(TV_Q251017,V_x))) = s(TV_Q251013,happ(s(t_fun(TV_Q251017,TV_Q251013),V_g),s(TV_Q251017,V_x))) => s(t_fun(TV_Q251017,TV_Q251013),V_f) = s(t_fun(TV_Q251017,TV_Q251013),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, 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))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_totos_allu_u_cpnu_u_distinctu_c5, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_greater) = s(t_h4s_totos_cpn,h4s_totos_equal))).
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_totou_u_glnequ_c1, conjecture, ![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_greater) => ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
