# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t0)),file('i/f/pred_set/PSUBSET__INSERT__SUBSET', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/PSUBSET__INSERT__SUBSET', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t0)|s(t_bool,X1)=s(t_bool,f)),file('i/f/pred_set/PSUBSET__INSERT__SUBSET', aHLu_BOOLu_CASES)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/pred_set/PSUBSET__INSERT__SUBSET', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X1]:(s(t_bool,t0)=s(t_bool,X1)<=>p(s(t_bool,X1))),file('i/f/pred_set/PSUBSET__INSERT__SUBSET', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(14, axiom,![X9]:![X1]:![X10]:(~(s(t_fun(X9,t_bool),X10)=s(t_fun(X9,t_bool),X1))<=>?[X6]:(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X1))))<=>~(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X10))))))),file('i/f/pred_set/PSUBSET__INSERT__SUBSET', ah4s_predu_u_sets_NOTu_u_EQUALu_u_SETS)).
fof(15, axiom,![X9]:![X1]:![X10]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X9,t_bool),X10),s(t_fun(X9,t_bool),X1))))<=>![X6]:(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X10))))=>p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X1)))))),file('i/f/pred_set/PSUBSET__INSERT__SUBSET', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(16, axiom,![X9]:![X1]:![X10]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X9,t_bool),X10),s(t_fun(X9,t_bool),X1))))<=>(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X9,t_bool),X10),s(t_fun(X9,t_bool),X1))))&~(s(t_fun(X9,t_bool),X10)=s(t_fun(X9,t_bool),X1)))),file('i/f/pred_set/PSUBSET__INSERT__SUBSET', ah4s_predu_u_sets_PSUBSETu_u_DEF)).
fof(17, axiom,![X9]:![X6]:![X1]:![X10]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X9,t_bool),h4s_predu_u_sets_insert(s(X9,X6),s(t_fun(X9,t_bool),X10))),s(t_fun(X9,t_bool),X1))))<=>(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X1))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X9,t_bool),X10),s(t_fun(X9,t_bool),X1)))))),file('i/f/pred_set/PSUBSET__INSERT__SUBSET', ah4s_predu_u_sets_INSERTu_u_SUBSET)).
fof(18, conjecture,![X9]:![X1]:![X10]:(p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(X9,t_bool),X10),s(t_fun(X9,t_bool),X1))))<=>?[X6]:(~(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X10)))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X9,t_bool),h4s_predu_u_sets_insert(s(X9,X6),s(t_fun(X9,t_bool),X10))),s(t_fun(X9,t_bool),X1)))))),file('i/f/pred_set/PSUBSET__INSERT__SUBSET', ch4s_predu_u_sets_PSUBSETu_u_INSERTu_u_SUBSET)).
# SZS output end CNFRefutation
