# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(s(t_h4s_fcps_cart(t_bool,X1),X2)=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))<=>![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))))=>~(p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,X1),X2),s(t_h4s_nums_num,X3))))))),file('i/f/words/word__eq__0', ch4s_wordss_wordu_u_equ_u_0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/words/word__eq__0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/words/word__eq__0', aHLu_FALSITY)).
fof(5, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/words/word__eq__0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(8, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/words/word__eq__0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/words/word__eq__0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(12, axiom,![X1]:![X12]:![X10]:![X7]:(s(t_h4s_fcps_cart(X1,X12),X7)=s(t_h4s_fcps_cart(X1,X12),X10)<=>![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X12),h4s_bools_theu_u_value))))))=>s(X1,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(X1,X12),X7),s(t_h4s_nums_num,X3)))=s(X1,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(X1,X12),X10),s(t_h4s_nums_num,X3))))),file('i/f/words/word__eq__0', ah4s_fcps_CARTu_u_EQ)).
fof(13, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/words/word__eq__0', aHLu_BOOLu_CASES)).
fof(15, axiom,![X1]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))))=>~(p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,X3)))))),file('i/f/words/word__eq__0', ah4s_wordss_wordu_u_0)).
# SZS output end CNFRefutation
