# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_bags_psubu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X3))))&p(s(t_bool,h4s_bags_psubu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X2)))))=>p(s(t_bool,h4s_bags_psubu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X2))))),file('i/f/bag/PSUB__BAG__TRANS', ch4s_bags_PSUBu_u_BAGu_u_TRANS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/PSUB__BAG__TRANS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/PSUB__BAG__TRANS', aHLu_FALSITY)).
fof(18, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/bag/PSUB__BAG__TRANS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(19, axiom,![X7]:(s(t_bool,X7)=s(t_bool,f)<=>~(p(s(t_bool,X7)))),file('i/f/bag/PSUB__BAG__TRANS', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(39, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/bag/PSUB__BAG__TRANS', aHLu_BOOLu_CASES)).
fof(42, axiom,![X1]:![X3]:![X4]:(p(s(t_bool,h4s_bags_psubu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X3))))<=>(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X3))))&~(s(t_fun(X1,t_h4s_nums_num),X4)=s(t_fun(X1,t_h4s_nums_num),X3)))),file('i/f/bag/PSUB__BAG__TRANS', ah4s_bags_PSUBu_u_BAG0)).
fof(45, axiom,![X1]:![X3]:![X4]:((p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X3))))&p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X4)))))=>s(t_fun(X1,t_h4s_nums_num),X4)=s(t_fun(X1,t_h4s_nums_num),X3)),file('i/f/bag/PSUB__BAG__TRANS', ah4s_bags_SUBu_u_BAGu_u_ANTISYM)).
fof(46, axiom,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X3))))&p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X2)))))=>p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X2))))),file('i/f/bag/PSUB__BAG__TRANS', ah4s_bags_SUBu_u_BAGu_u_TRANS)).
# SZS output end CNFRefutation
