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__11,axiom,(![V0a0_2E0, V1a1_2E0, V2a0_27_2E0, V3a1_27_2E0]: ((s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EConjn_2E2(s(tyop_2EDeepSyntax_2Edeep__form,V0a0_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V1a1_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EConjn_2E2(s(tyop_2EDeepSyntax_2Edeep__form,V2a0_27_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V3a1_27_2E0)))) <=> ((s(tyop_2EDeepSyntax_2Edeep__form,V0a0_2E0) = s(tyop_2EDeepSyntax_2Edeep__form,V2a0_27_2E0)) & (s(tyop_2EDeepSyntax_2Edeep__form,V1a1_2E0) = s(tyop_2EDeepSyntax_2Edeep__form,V3a1_27_2E0)))) & (![V4a0_2E0, V5a1_2E0, V6a0_27_2E0, V7a1_27_2E0]: ((s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EDisjn_2E2(s(tyop_2EDeepSyntax_2Edeep__form,V4a0_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V5a1_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EDisjn_2E2(s(tyop_2EDeepSyntax_2Edeep__form,V6a0_27_2E0),s(tyop_2EDeepSyntax_2Edeep__form,V7a1_27_2E0)))) <=> ((s(tyop_2EDeepSyntax_2Edeep__form,V4a0_2E0) = s(tyop_2EDeepSyntax_2Edeep__form,V6a0_27_2E0)) & (s(tyop_2EDeepSyntax_2Edeep__form,V5a1_2E0) = s(tyop_2EDeepSyntax_2Edeep__form,V7a1_27_2E0)))) & (![V8a_2E0, V9a_27_2E0]: ((s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ENegn_2E1(s(tyop_2EDeepSyntax_2Edeep__form,V8a_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ENegn_2E1(s(tyop_2EDeepSyntax_2Edeep__form,V9a_27_2E0)))) <=> (s(tyop_2EDeepSyntax_2Edeep__form,V8a_2E0) = s(tyop_2EDeepSyntax_2Edeep__form,V9a_27_2E0))) & (![V10a_2E0, V11a_27_2E0]: ((s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EUnrelatedBool_2E1(s(tyop_2Emin_2Ebool,V10a_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2EUnrelatedBool_2E1(s(tyop_2Emin_2Ebool,V11a_27_2E0)))) <=> (s(tyop_2Emin_2Ebool,V10a_2E0) = s(tyop_2Emin_2Ebool,V11a_27_2E0))) & (![V12a_2E0, V13a_27_2E0]: ((s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExLT_2E1(s(tyop_2Einteger_2Eint,V12a_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExLT_2E1(s(tyop_2Einteger_2Eint,V13a_27_2E0)))) <=> (s(tyop_2Einteger_2Eint,V12a_2E0) = s(tyop_2Einteger_2Eint,V13a_27_2E0))) & (![V14a_2E0, V15a_27_2E0]: ((s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ELTx_2E1(s(tyop_2Einteger_2Eint,V14a_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ELTx_2E1(s(tyop_2Einteger_2Eint,V15a_27_2E0)))) <=> (s(tyop_2Einteger_2Eint,V14a_2E0) = s(tyop_2Einteger_2Eint,V15a_27_2E0))) & (![V16a_2E0, V17a_27_2E0]: ((s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExEQ_2E1(s(tyop_2Einteger_2Eint,V16a_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExEQ_2E1(s(tyop_2Einteger_2Eint,V17a_27_2E0)))) <=> (s(tyop_2Einteger_2Eint,V16a_2E0) = s(tyop_2Einteger_2Eint,V17a_27_2E0))) & ![V18a0_2E0, V19a1_2E0, V20a0_27_2E0, V21a1_27_2E0]: ((s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExDivided_2E2(s(tyop_2Einteger_2Eint,V18a0_2E0),s(tyop_2Einteger_2Eint,V19a1_2E0))) = s(tyop_2EDeepSyntax_2Edeep__form,c_2EDeepSyntax_2ExDivided_2E2(s(tyop_2Einteger_2Eint,V20a0_27_2E0),s(tyop_2Einteger_2Eint,V21a1_27_2E0)))) <=> ((s(tyop_2Einteger_2Eint,V18a0_2E0) = s(tyop_2Einteger_2Eint,V20a0_27_2E0)) & (s(tyop_2Einteger_2Eint,V19a1_2E0) = s(tyop_2Einteger_2Eint,V21a1_27_2E0)))))))))))).
