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_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X1_2E0))))).
fof(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27e_29_20mono_2EA_27f_20mono_2EA_27g,axiom,![A_27a, A_27b, A_27d, A_27e, A_27f, A_27g]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0))))).
fof(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27f_20mono_2EA_27g_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e,axiom,![A_27c, A_27d, A_27e, A_27f, A_27g]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X1_2E0))))).
fof(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27f_20mono_2EA_27g,axiom,![A_27a, A_27b, A_27c, A_27f, A_27g]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0))))).
fof(errorStateMonadTheory_2EMCOMP__ASSOC,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e, A_27f, A_27g]: ![V0h_2E0, V1g_2E0, V2f_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),V0h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),V2f_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),V0h_2E0))))).
