# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:((p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X2))),s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5))))&p(s(t_bool,h4s_setu_u_relations_strictu_u_linearu_u_order(s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5),s(t_fun(X1,t_bool),X4)))))=>(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4))))&p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X4)))))),file('i/f/set_relation/strict__linear__order__dom__rng', ch4s_setu_u_relations_strictu_u_linearu_u_orderu_u_domu_u_rng)).
fof(2, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/set_relation/strict__linear__order__dom__rng', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(6, axiom,![X1]:![X2]:![X3]:![X5]:(p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X2))),s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5))))=>p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X2))),s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),h4s_setu_u_relations_tc(s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5))))))),file('i/f/set_relation/strict__linear__order__dom__rng', ah4s_setu_u_relations_tcu_u_rulesu_c0)).
fof(37, axiom,![X1]:![X28]:![X20]:(?[X3]:(s(X1,X3)=s(X1,X28)&p(s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X3)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X28))))),file('i/f/set_relation/strict__linear__order__dom__rng', ah4s_bools_UNWINDu_u_THM2)).
fof(52, axiom,![X1]:![X29]:![X30]:(![X3]:(s(X1,X3)=s(X1,X29)=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X30),s(X1,X3)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X30),s(X1,X29))))),file('i/f/set_relation/strict__linear__order__dom__rng', ah4s_bools_UNWINDu_u_FORALLu_u_THM2)).
fof(57, axiom,![X1]:![X3]:![X20]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X20)))=s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X3))),file('i/f/set_relation/strict__linear__order__dom__rng', ah4s_predu_u_sets_SPECIFICATION)).
fof(61, axiom,![X1]:![X4]:![X5]:(p(s(t_bool,h4s_setu_u_relations_strictu_u_linearu_u_order(s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5),s(t_fun(X1,t_bool),X4))))<=>(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_setu_u_relations_domain(s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5))),s(t_fun(X1,t_bool),X4))))&(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_setu_u_relations_range(s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5))),s(t_fun(X1,t_bool),X4))))&(p(s(t_bool,h4s_setu_u_relations_transitive(s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5))))&(![X3]:~(p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X3))),s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5)))))&![X3]:![X2]:((p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4))))&(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X4))))&~(s(X1,X3)=s(X1,X2))))=>(p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X2))),s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5))))|p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X2),s(X1,X3))),s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5))))))))))),file('i/f/set_relation/strict__linear__order__dom__rng', ah4s_setu_u_relations_strictu_u_linearu_u_orderu_u_def)).
fof(64, axiom,![X1]:![X2]:![X3]:![X5]:(p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X1),h4s_pairs_u_2c(s(X1,X3),s(X1,X2))),s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),h4s_setu_u_relations_tc(s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5))))))=>(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_setu_u_relations_domain(s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5))))))&p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_setu_u_relations_range(s(t_fun(t_h4s_pairs_prod(X1,X1),t_bool),X5)))))))),file('i/f/set_relation/strict__linear__order__dom__rng', ah4s_setu_u_relations_tcu_u_domainu_u_range)).
fof(69, axiom,![X1]:![X15]:![X4]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X15))))<=>![X3]:(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4))))=>p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X15)))))),file('i/f/set_relation/strict__linear__order__dom__rng', ah4s_predu_u_sets_SUBSETu_u_DEF)).
# SZS output end CNFRefutation
