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(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,![A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ECONS_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))))).
fof(arityeq1_2Ec_2Estate__transformer_2EUNIT_2E1_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))))).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0))))).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0))))).
fof(arityeq2_2Ec_2Elist_2EFOLDR_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27b_29_2CA_27a_29_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Elist_2EFOLDR_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),X1_2E0))))).
fof(state__transformerTheory_2Esequence__def,axiom,![A_27a, A_27b]: ![F2_2E0, F1_2E0, F0_2E0]: (![V2x_2E0, V3xs_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F2_2E0),s(A_27b,V2x_2E0))),s(tyop_2Elist_2Elist(A_27b),V3xs_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2x_2E0),s(tyop_2Elist_2Elist(A_27b),V3xs_2E0)))))) => (![V1ms_2E0, V2x_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),V1ms_2E0))),s(A_27b,V2x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),V1ms_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F2_2E0),s(A_27b,V2x_2E0)))))) => (![V0m_2E0, V1ms_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),V1ms_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0m_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),V1ms_2E0)))))) => (s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Estate__transformer_2Esequence_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Elist_2EFOLDR_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))))))).
