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_2Eintegration_2Elifted_2E1_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal))),c_2Eintegration_2Elifted_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal)))),c_2Eintegration_2Elifted_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),X0_2E0))))).
fof(arityeq2_2Ec_2Eintegration_2Eoperative_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Erealax_2Ereal_29,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Eintegration_2Eoperative_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool)),c_2Eintegration_2Eoperative_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal)),X1_2E0))))).
fof(arityeq2_2Ec_2Eintegration_2Eoperative_2E2_2Emono_2Etyop_2Erealax_2Ereal,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Eintegration_2Eoperative_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool)),c_2Eintegration_2Eoperative_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),X1_2E0))))).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Erealax_2Ereal_29,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),X2_2E0))))).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,![X0_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),c_2Eoption_2ESOME_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal)),c_2Eoption_2ESOME_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))))).
fof(arityeq2_2Ec_2Eintegration_2Ehas__bounded__setvariation__on_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Eintegration_2Ehas__bounded__setvariation__on_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eintegration_2Ehas__bounded__setvariation__on_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Eintegration_2Eset__variation_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Erealax_2Ereal,c_2Eintegration_2Eset__variation_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal)),c_2Eintegration_2Eset__variation_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),X1_2E0))))).
fof(integrationTheory_2EOPERATIVE__LIFTED__SETVARIATION,axiom,![F0_2E0]: (![V0f_2E0, V1i_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1i_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eintegration_2Ehas__bounded__setvariation__on_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1i_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),c_2Eoption_2ESOME_2E1(s(tyop_2Erealax_2Ereal,c_2Eintegration_2Eset__variation_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V0f_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),c_2Eoption_2ENONE_2E0)))) => ![V0f_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Eintegration_2Eoperative_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Erealax_2Ereal__add_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V0f_2E0)))) => p(s(tyop_2Emin_2Ebool,c_2Eintegration_2Eoperative_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal))),c_2Eintegration_2Elifted_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Erealax_2Ereal__add_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Erealax_2Ereal))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal),V0f_2E0))))))))).
