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_2EDeepSyntax_2ELTx_2E1,axiom,![X0_2E0]: (s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ELTx_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),c_2EDeepSyntax_2ELTx_2E0),s(tyop_2Einteger_2Eint,X0_2E0))))).
fof(arityeq1_2Ec_2EDeepSyntax_2ENegn_2E1,axiom,![X0_2E0]: (s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ENegn_2E1(s(tyop_2EDeepSyntax_2Edeep__form,X0_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form),c_2EDeepSyntax_2ENegn_2E0),s(tyop_2EDeepSyntax_2Edeep__form,X0_2E0))))).
fof(arityeq1_2Ec_2EDeepSyntax_2EUnrelatedBool_2E1,axiom,![X0_2E0]: (s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EUnrelatedBool_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2EDeepSyntax_2Edeep__form),c_2EDeepSyntax_2EUnrelatedBool_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))).
fof(arityeq1_2Ec_2EDeepSyntax_2ExEQ_2E1,axiom,![X0_2E0]: (s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExEQ_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),c_2EDeepSyntax_2ExEQ_2E0),s(tyop_2Einteger_2Eint,X0_2E0))))).
fof(arityeq1_2Ec_2EDeepSyntax_2ExLT_2E1,axiom,![X0_2E0]: (s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExLT_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),c_2EDeepSyntax_2ExLT_2E0),s(tyop_2Einteger_2Eint,X0_2E0))))).
fof(arityeq2_2Ec_2EDeepSyntax_2EConjn_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EConjn_2E2(s(tyop_2EDeepSyntax_2Edeep__form,X0_2E0),s(tyop_2EDeepSyntax_2Edeep__form,X1_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form),app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form)),c_2EDeepSyntax_2EConjn_2E0),s(tyop_2EDeepSyntax_2Edeep__form,X0_2E0))),s(tyop_2EDeepSyntax_2Edeep__form,X1_2E0))))).
fof(arityeq2_2Ec_2EDeepSyntax_2EDisjn_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EDisjn_2E2(s(tyop_2EDeepSyntax_2Edeep__form,X0_2E0),s(tyop_2EDeepSyntax_2Edeep__form,X1_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form),app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2EDeepSyntax_2Edeep__form)),c_2EDeepSyntax_2EDisjn_2E0),s(tyop_2EDeepSyntax_2Edeep__form,X0_2E0))),s(tyop_2EDeepSyntax_2Edeep__form,X1_2E0))))).
fof(arityeq2_2Ec_2EDeepSyntax_2ExDivided_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExDivided_2E2(s(tyop_2Einteger_2Eint,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2EDeepSyntax_2Edeep__form)),c_2EDeepSyntax_2ExDivided_2E0),s(tyop_2Einteger_2Eint,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))))).
fof(DeepSyntaxTheory_2Edeep__form__induction,axiom,![V0P_2E0]: ((![V1d_2E0, V2d0_2E0]: ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V1d_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V2d0_2E0))))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EConjn_2E2(s(tyop_2EDeepSyntax_2Edeep__form,V1d_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V2d0_2E0))))))) & (![V3d_2E0, V4d0_2E0]: ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V3d_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V4d0_2E0))))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EDisjn_2E2(s(tyop_2EDeepSyntax_2Edeep__form,V3d_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V4d0_2E0))))))) & (![V5d_2E0]: (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V5d_2E0)))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ENegn_2E1(s(tyop_2EDeepSyntax_2Edeep__form,V5d_2E0))))))) & (![V6b_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EUnrelatedBool_2E1(s(tyop_2Emin_2Ebool,V6b_2E0)))))) & (![V7i_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExLT_2E1(s(tyop_2Einteger_2Eint,V7i_2E0)))))) & (![V8i_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ELTx_2E1(s(tyop_2Einteger_2Eint,V8i_2E0)))))) & (![V9i_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExEQ_2E1(s(tyop_2Einteger_2Eint,V9i_2E0)))))) & ![V10i_2E0, V11i0_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExDivided_2E2(s(tyop_2Einteger_2Eint,V10i_2E0),s(tyop_2Einteger_2Eint,V11i0_2E0))))))))))))) => ![V12d_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EDeepSyntax_2Edeep__form,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V12d_2E0)))))).
