fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Estring_2EEXPLODE_2E1,axiom,![X0_2E0]: (s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Estring_2EEXPLODE_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))))).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Elist_2ECONS_2E0),s(tyop_2Estring_2Echar,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X1_2E0))))).
fof(arityeq1_2Ec_2Estring_2EDEST__STRING_2E1,axiom,![X0_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Estring_2EDEST__STRING_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0))))).
fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X2_2E0))))).
fof(stringTheory_2EEXPLODE__DEST__STRING,axiom,![F1_2E0, F0_2E0]: (![V2c_2E0, V3t_2E0]: (s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),F1_2E0),s(tyop_2Estring_2Echar,V2c_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3t_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ECONS_2E2(s(tyop_2Estring_2Echar,V2c_2E0),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V3t_2E0)))))) => (![V1v_2E0]: (s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V1v_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),V1v_2E0),s(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),F1_2E0)))) => ![V0s_2E0]: (s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2EEXPLODE_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))) = s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Estring_2EDEST__STRING_2E1(s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0s_2E0))),s(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Estring_2Echar,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),F0_2E0))))))).
