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_2Earithmetic_2E_2B_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))))).
fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27input_20mono_2EA_27state,axiom,![A_27input, A_27state]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27input,A_27state),c_2Epair_2E_2C_2E2(s(A_27input,X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27input,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27input,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27input,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27input,A_27state))),c_2Epair_2E_2C_2E0),s(A_27input,X0_2E0))),s(A_27state,X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27input_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27state_29,axiom,![A_27input, A_27state]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),X1_2E0))))).
fof(Omega__AutomataTheory_2ENEG__DET__AUTOMATA,axiom,![A_27input, A_27state]: ![F1_2E0, F0_2E0]: (![V8q_2E0, V4t0_2E0, V10t_2E0]: (s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V8q_2E0))),s(tyop_2Enum_2Enum,V4t0_2E0))),s(tyop_2Enum_2Enum,V10t_2E0))) = s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V8q_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V10t_2E0),s(tyop_2Enum_2Enum,V4t0_2E0)))))) => (![V5q_2E0, V4t0_2E0, V7t_2E0]: (s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V5q_2E0))),s(tyop_2Enum_2Enum,V4t0_2E0))),s(tyop_2Enum_2Enum,V7t_2E0))) = s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V5q_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V7t_2E0),s(tyop_2Enum_2Enum,V4t0_2E0)))))) => ![V0Accept_2E0, V1i_2E0, V2TransRel_2E0, V3InitVal_2E0, V4t0_2E0]: (~ (?[V5q_2E0]: ((s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V5q_2E0),s(tyop_2Enum_2Enum,V4t0_2E0))) = s(A_27state,V3InitVal_2E0)) & (![V6t_2E0]: (s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V5q_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V6t_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V4t0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))) = s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27input,A_27state),A_27state),V2TransRel_2E0),s(tyop_2Epair_2Eprod(A_27input,A_27state),c_2Epair_2E_2C_2E2(s(A_27input,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V6t_2E0),s(tyop_2Enum_2Enum,V4t0_2E0))))),s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V5q_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V6t_2E0),s(tyop_2Enum_2Enum,V4t0_2E0)))))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),tyop_2Emin_2Ebool),V0Accept_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V5q_2E0))),s(tyop_2Enum_2Enum,V4t0_2E0))))))))))) <=> ?[V8q_2E0]: ((s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V8q_2E0),s(tyop_2Enum_2Enum,V4t0_2E0))) = s(A_27state,V3InitVal_2E0)) & (![V9t_2E0]: (s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V8q_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V9t_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V4t0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))) = s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27input,A_27state),A_27state),V2TransRel_2E0),s(tyop_2Epair_2Eprod(A_27input,A_27state),c_2Epair_2E_2C_2E2(s(A_27input,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V9t_2E0),s(tyop_2Enum_2Enum,V4t0_2E0))))),s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V8q_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V9t_2E0),s(tyop_2Enum_2Enum,V4t0_2E0)))))))))) & ~ (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),tyop_2Emin_2Ebool),V0Accept_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V8q_2E0))),s(tyop_2Enum_2Enum,V4t0_2E0))))))))))))))).
