# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:~(s(t_h4s_fcps_bit1(X1),happ(s(t_fun(X1,t_h4s_fcps_bit1(X1)),h4s_fcps_bit1a),s(X1,X3)))=s(t_h4s_fcps_bit1(X1),happ(s(t_fun(X1,t_h4s_fcps_bit1(X1)),h4s_fcps_bit1b),s(X1,X2)))),file('i/f/fcp/bit1__distinct_c0', ch4s_fcps_bit1u_u_distinctu_c0)).
fof(3, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/fcp/bit1__distinct_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X1]:![X18]:![X6]:(![X8]:(s(X1,X8)=s(X1,X18)=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X6),s(X1,X8)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X6),s(X1,X18))))),file('i/f/fcp/bit1__distinct_c0', ah4s_bools_UNWINDu_u_FORALLu_u_THM2)).
fof(33, axiom,![X1]:![X8]:![X26]:s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X26)))=s(t_bool,happ(s(t_fun(X1,t_bool),X26),s(X1,X8))),file('i/f/fcp/bit1__distinct_c0', ah4s_bools_INu_u_DEF)).
fof(34, axiom,![X1]:s(t_fun(X1,t_h4s_fcps_bit1(X1)),h4s_fcps_bit1b)=s(t_fun(X1,t_h4s_fcps_bit1(X1)),h4s_fcps_u_20u_40indu_u_typefcp5),file('i/f/fcp/bit1__distinct_c0', ah4s_fcps_BIT1B0)).
fof(36, axiom,![X1]:![X2]:![X3]:(s(t_h4s_fcps_bit1(X1),happ(s(t_fun(X1,t_h4s_fcps_bit1(X1)),h4s_fcps_bit1b),s(X1,X3)))=s(t_h4s_fcps_bit1(X1),happ(s(t_fun(X1,t_h4s_fcps_bit1(X1)),h4s_fcps_bit1b),s(X1,X2)))<=>s(X1,X3)=s(X1,X2)),file('i/f/fcp/bit1__distinct_c0', ah4s_fcps_bit1u_u_11u_c1)).
fof(38, axiom,![X12]:![X1]:![X18]:![X28]:![X6]:![X3]:s(X12,h4s_fcps_bit1u_u_case(s(t_h4s_fcps_bit1(X1),happ(s(t_fun(X1,t_h4s_fcps_bit1(X1)),h4s_fcps_bit1b),s(X1,X3))),s(t_fun(X1,X12),X6),s(t_fun(X1,X12),X28),s(X12,X18)))=s(X12,happ(s(t_fun(X1,X12),X28),s(X1,X3))),file('i/f/fcp/bit1__distinct_c0', ah4s_fcps_bit1u_u_caseu_u_defu_c1)).
fof(40, axiom,![X1]:s(t_fun(X1,t_h4s_fcps_bit1(X1)),h4s_fcps_bit1a)=s(t_fun(X1,t_h4s_fcps_bit1(X1)),h4s_fcps_u_20u_40indu_u_typefcp4),file('i/f/fcp/bit1__distinct_c0', ah4s_fcps_BIT1A0)).
fof(42, axiom,![X12]:![X1]:![X18]:![X28]:![X6]:![X3]:s(X12,h4s_fcps_bit1u_u_case(s(t_h4s_fcps_bit1(X1),happ(s(t_fun(X1,t_h4s_fcps_bit1(X1)),h4s_fcps_bit1a),s(X1,X3))),s(t_fun(X1,X12),X6),s(t_fun(X1,X12),X28),s(X12,X18)))=s(X12,happ(s(t_fun(X1,X12),X6),s(X1,X3))),file('i/f/fcp/bit1__distinct_c0', ah4s_fcps_bit1u_u_caseu_u_defu_c0)).
fof(43, axiom,p(s(t_bool,t)),file('i/f/fcp/bit1__distinct_c0', aHLu_TRUTH)).
fof(46, axiom,![X11]:(s(t_bool,t)=s(t_bool,X11)<=>p(s(t_bool,X11))),file('i/f/fcp/bit1__distinct_c0', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(55, axiom,~(p(s(t_bool,f))),file('i/f/fcp/bit1__distinct_c0', aHLu_FALSITY)).
fof(57, axiom,(p(s(t_bool,f))<=>![X11]:p(s(t_bool,X11))),file('i/f/fcp/bit1__distinct_c0', ah4s_bools_Fu_u_DEF)).
fof(58, axiom,![X11]:(s(t_bool,f)=s(t_bool,X11)<=>~(p(s(t_bool,X11)))),file('i/f/fcp/bit1__distinct_c0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(78, axiom,![X1]:![X13]:![X8]:![X34]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X34),s(X1,X13))),s(X1,X8))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X34))))&~(s(X1,X8)=s(X1,X13)))),file('i/f/fcp/bit1__distinct_c0', ah4s_predu_u_sets_DELETEu_u_applied)).
fof(81, axiom,![X1]:![X13]:![X8]:![X34]:(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X13),s(t_fun(X1,t_bool),X34))))))<=>(s(X1,X8)=s(X1,X13)|p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X34)))))),file('i/f/fcp/bit1__distinct_c0', ah4s_predu_u_sets_INu_u_INSERT)).
# SZS output end CNFRefutation
