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_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27state,axiom,![A_27a, A_27state]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27state,X1_2E0))))).
fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27state,axiom,![A_27b, A_27state]: ![X0_2E0]: (s(A_27state,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27state),X0_2E0))) = s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),A_27state),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),X0_2E0))))).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29,axiom,![A_27a, A_27state]: ![X0_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27state),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27state),X0_2E0))))).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27state_29_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29,axiom,![A_27a, A_27b, A_27state]: ![X0_2E0, X1_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),X1_2E0))))).
fof(arityeq3_2Ec_2EerrorStateMonad_2ENARROW_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state,axiom,![A_27a, A_27b, A_27state]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2EerrorStateMonad_2ENARROW_2E3(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X1_2E0),s(A_27state,X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))))),c_2EerrorStateMonad_2ENARROW_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X1_2E0))),s(A_27state,X2_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27state,axiom,![A_27b, A_27state]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27b,A_27state),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27state,X1_2E0))))).
fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27state_29_29,axiom,![A_27a, A_27b, A_27state]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X2_2E0))))).
fof(errorStateMonadTheory_2ENARROW__def,axiom,![A_27a, A_27b, A_27state]: ![F1_2E0, F0_2E0]: (![V4r_2E0, V5s1_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),F1_2E0),s(A_27a,V4r_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27state),V5s1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2E_2C_2E2(s(A_27a,V4r_2E0),s(A_27state,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27state),V5s1_2E0)))))))) => (![V3v_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),F0_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),V3v_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),V3v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),F1_2E0)))) => ![V0v_2E0, V1f_2E0, V2x_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2EerrorStateMonad_2ENARROW_2E3(s(A_27b,V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),V1f_2E0),s(A_27state,V2x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),V1f_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),c_2Epair_2E_2C_2E2(s(A_27b,V0v_2E0),s(A_27state,V2x_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),F0_2E0))))))).
