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(arityeq3_2Ec_2Esum_2ESUM__MAP_2E3_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b, A_27c, A_27d]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2ESUM__MAP_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0),s(tyop_2Esum_2Esum(A_27c,A_27d),X2_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27a,A_27b)))),c_2Esum_2ESUM__MAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0))),s(tyop_2Esum_2Esum(A_27c,A_27d),X2_2E0))))).
fof(arityeq3_2Ec_2Esum_2ESUM__MAP_2E3_2Emono_2EA_27e_20mono_2EA_27f_20mono_2EA_27c_20mono_2EA_27d,axiom,![A_27c, A_27d, A_27e, A_27f]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2ESUM__MAP_2E3(s(tyop_2Emin_2Efun(A_27e,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27f,A_27d),X1_2E0),s(tyop_2Esum_2Esum(A_27e,A_27f),X2_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Esum_2ESUM__MAP_2E0),s(tyop_2Emin_2Efun(A_27e,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27f,A_27d),X1_2E0))),s(tyop_2Esum_2Esum(A_27e,A_27f),X2_2E0))))).
fof(arityeq3_2Ec_2Esum_2ESUM__MAP_2E3_2Emono_2EA_27e_20mono_2EA_27f_20mono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b, A_27e, A_27f]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2ESUM__MAP_2E3(s(tyop_2Emin_2Efun(A_27e,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27f,A_27b),X1_2E0),s(tyop_2Esum_2Esum(A_27e,A_27f),X2_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27a,A_27b)))),c_2Esum_2ESUM__MAP_2E0),s(tyop_2Emin_2Efun(A_27e,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27f,A_27b),X1_2E0))),s(tyop_2Esum_2Esum(A_27e,A_27f),X2_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27e_20mono_2EA_27a_20mono_2EA_27c,axiom,![A_27a, A_27c, A_27e]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27e,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27e,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27e,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27c),tyop_2Emin_2Efun(A_27e,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27c),tyop_2Emin_2Efun(A_27e,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27e,A_27c),X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27f_20mono_2EA_27b_20mono_2EA_27d,axiom,![A_27b, A_27d, A_27f]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27f,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27f,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27f,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27f,A_27d),X1_2E0))))).
fof(namespace__tagTheory_2Esumpp__compose,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e, A_27f]: ![V0x_2E0, V1b_2E0, V2a_2E0, V3g_2E0, V4f_2E0]: (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2ESUM__MAP_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V4f_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V3g_2E0),s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2ESUM__MAP_2E3(s(tyop_2Emin_2Efun(A_27e,A_27c),V2a_2E0),s(tyop_2Emin_2Efun(A_27f,A_27d),V1b_2E0),s(tyop_2Esum_2Esum(A_27e,A_27f),V0x_2E0))))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2ESUM__MAP_2E3(s(tyop_2Emin_2Efun(A_27e,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V4f_2E0),s(tyop_2Emin_2Efun(A_27e,A_27c),V2a_2E0))),s(tyop_2Emin_2Efun(A_27f,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V3g_2E0),s(tyop_2Emin_2Efun(A_27f,A_27d),V1b_2E0))),s(tyop_2Esum_2Esum(A_27e,A_27f),V0x_2E0))))).
