fof(reserved_2Eho_2Eeq__ext,axiom,![A_27a, A_27b]: ![V0f_2E0, V1g_2E0]: (![V2x_2E0]: (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) => (s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0)))).
fof(reserved_2Eho_2Eboolext,axiom,![V0_2E0, V1_2E0]: ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <=> p(s(tyop_2Emin_2Ebool,V1_2E0))) => (s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0)))).
fof(reserved_2Eho_2Etruth,axiom,p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))).
fof(reserved_2Eho_2Enotfalse,axiom,~ (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,![V0t_2E0]: ((s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) | (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))).
fof(reserved_2Eho_2Ei__thm,axiom,![A_27a]: ![V0x_2E0]: (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0))).
fof(reserved_2Eho_2Ek__thm,axiom,![A_27a, A_27b]: ![V0x_2E0, V1y_2E0]: (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0))).
fof(reserved_2Eho_2Es__thm,axiom,![A_27a, A_27b, A_27c]: ![V0f_2E0, V1g_2E0, V2x_2E0]: (s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))))).
fof(reserved_2Elogic_2E_2F_5C,axiom,![V0_2E0, V1_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <=> (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0))))).
fof(reserved_2Elogic_2E_5C_2F,axiom,![V0_2E0, V1_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <=> (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0))))).
fof(reserved_2Elogic_2E_7E,axiom,![V0_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <=> ~ (p(s(tyop_2Emin_2Ebool,V0_2E0))))).
fof(reserved_2Elogic_2E_3D_3D_3E,axiom,![V0_2E0, V1_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <=> (p(s(tyop_2Emin_2Ebool,V0_2E0)) => p(s(tyop_2Emin_2Ebool,V1_2E0))))).
fof(reserved_2Elogic_2E_3D,axiom,![A_27a]: ![V0_2E0, V1_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <=> (s(A_27a,V0_2E0) = s(A_27a,V1_2E0)))).
fof(reserved_2Equant_2E_21,axiom,![A_27a]: ![V0f_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <=> ![V1x_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))))).
fof(reserved_2Equant_2E_3F,axiom,![A_27a]: ![V0f_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <=> ?[V1x_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))))).
